In Canada, criminal law is national law rather than provincial law.
There are several categories of justification of use of form in Canadian criminal law, including aiding a peace officer at the officer's direction, which are comprehensively summarized in the following statutory sections.
The Canadian criminal code states (also here and here) (emphasis and captions not indented are mine):
General Principles
25 (1) Every one who is required or authorized by law to do anything
in the administration or enforcement of the law
(a) as a private person,
(b) as a peace officer or public officer,
(c) in aid of a peace officer or public officer, or
(d) by virtue of his office,
is, if he acts on reasonable grounds, justified in doing what he is
required or authorized to do and in using as much force as is
necessary for that purpose.
(2) Where a person is required or authorized by law to execute a
process or to carry out a sentence, that person or any person who
assists him is, if that person acts in good faith, justified in
executing the process or in carrying out the sentence notwithstanding
that the process or sentence is defective or that it was issued or
imposed without jurisdiction or in excess of jurisdiction.
(3) Subject to subsections (4) and (5), a person is not justified for
the purposes of subsection (1) in using force that is intended or is
likely to cause death or grievous bodily harm unless the person
believes on reasonable grounds that it is necessary for the
self-preservation of the person or the preservation of any one under
that person’s protection from death or grievous bodily harm.
(4) A peace officer, and every person lawfully assisting the peace
officer, is justified in using force that is intended or is likely to
cause death or grievous bodily harm to a person to be arrested, if
(a) the peace officer is proceeding lawfully to arrest, with or
without warrant, the person to be arrested;
(b) the offence for which the person is to be arrested is one for
which that person may be arrested without warrant;
(c) the person to be arrested takes flight to avoid arrest;
(d) the peace officer or other person using the force believes on
reasonable grounds that the force is necessary for the purpose of
protecting the peace officer, the person lawfully assisting the peace
officer or any other person from imminent or future death or grievous
bodily harm; and
(e) the flight cannot be prevented by reasonable means in a less
violent manner. . . .
25.1 (1) The following definitions apply in this section and sections 25.2 to 25.4. . . .
(10) A person who commits an act or omission that would otherwise
constitute an offence is justified in committing it if
(a) a public officer directs him or her to commit that act or omission
and the person believes on reasonable grounds that the public officer
has the authority to give that direction; and
(b) he or she believes on reasonable grounds that the commission of
that act or omission is for the purpose of assisting the public
officer in the public officer’s law enforcement duties.
(11) Nothing in this section justifies
(a) the intentional or criminally negligent causing of death or bodily
harm to another person;
(b) the wilful attempt in any manner to obstruct, pervert or defeat
the course of justice; or
(c) conduct that would violate the sexual integrity of an individual.
(12) Nothing in this section affects the protection, defences and
immunities of peace officers and other persons recognized under the
law of Canada. . . .
26 Every one who is authorized by law to use force is criminally
responsible for any excess thereof according to the nature and quality
of the act that constitutes the excess.
Use Of Force To Prevent A Crime
27 Every one is justified in using as much force as is reasonably
necessary
(a) to prevent the commission of an offence
(i) for which, if it were committed, the person who committed it might
be arrested without warrant, and
(ii) that would be likely to cause immediate and serious injury to the
person or property of anyone; or
(b) to prevent anything being done that, on reasonable grounds, he
believes would, if it were done, be an offence mentioned in paragraph
(a).
Use Of Force On Aircraft In Flight
27.1 (1) Every person on an aircraft in flight is justified in using as much force as is reasonably necessary to prevent the commission of
an offence against this Act or another Act of Parliament that the
person believes on reasonable grounds, if it were committed, would be
likely to cause immediate and serious injury to the aircraft or to any
person or property therein.
(2) This section applies in respect of any aircraft in flight in
Canadian airspace and in respect of any aircraft registered in Canada
in accordance with the regulations made under the Aeronautics Act in
flight outside Canadian airspace.
Use Of Force To Carry Out An Arrest Warrant
28 (1) Where a person who is authorized to execute a warrant to
arrest believes, in good faith and on reasonable grounds, that the
person whom he arrests is the person named in the warrant, he is
protected from criminal responsibility in respect thereof to the same
extent as if that person were the person named in the warrant.
(2) Where a person is authorized to execute a warrant to arrest,
(a) every one who, being called on to assist him, believes that the
person in whose arrest he is called on to assist is the person named
in the warrant, . . .
is protected from criminal responsibility in respect thereof to the
same extent as if that person were the person named in the warrant.
29 (1) It is the duty of every one who executes a process or warrant
to have it with him, where it is feasible to do so, and to produce it
when requested to do so.
(2) It is the duty of every one who arrests a person, whether with or
without a warrant, to give notice to that person, where it is feasible
to do so, of
(a) the process or warrant under which he makes the arrest; or
(b) the reason for the arrest.
(3) Failure to comply with subsection (1) or (2) does not of itself
deprive a person who executes a process or warrant, or a person who
makes an arrest, or those who assist them, of protection from criminal
responsibility.
Use Of Force To Stop Breach Of The Peace
30 Every one who witnesses a breach of the peace is justified in
interfering to prevent the continuance or renewal thereof and may
detain any person who commits or is about to join in or to renew the
breach of the peace, for the purpose of giving him into the custody of
a peace officer, if he uses no more force than is reasonably necessary
to prevent the continuance or renewal of the breach of the peace or
than is reasonably proportioned to the danger to be apprehended from
the continuance or renewal of the breach of the peace.
31 (1) Every peace officer who witnesses a breach of the peace and
every one who lawfully assists the peace officer is justified in
arresting any person whom he finds committing the breach of the peace
or who, on reasonable grounds, he believes is about to join in or
renew the breach of the peace.
(2) Every peace officer is justified in receiving into custody any
person who is given into his charge as having been a party to a breach
of the peace by one who has, or who on reasonable grounds the peace
officer believes has, witnessed the breach of the peace.
Use of Force To Suppress A Riot
32 . . .
(4) Every one who, in good faith and on reasonable grounds, believes
that serious mischief will result from a riot before it is possible to
secure the attendance of a peace officer is justified in using as much
force as he believes in good faith and on reasonable grounds,
(a) is necessary to suppress the riot; and
(b) is not excessive, having regard to the danger to be apprehended
from the continuance of the riot.
(5) For the purposes of this section, the question whether an order is
manifestly unlawful or not is a question of law.
33 (1) Where the proclamation referred to in section 67 has been made
or an offence against paragraph 68(a) or (b) has been committed, it is
the duty of a peace officer and of a person who is lawfully required
by him to assist, to disperse or to arrest persons who do not comply
with the proclamation.
(2) No civil or criminal proceedings lie against a peace officer or a
person who is lawfully required by a peace officer to assist him in
respect of any death or injury that by reason of resistance is caused
as a result of the performance by the peace officer or that person of
a duty that is imposed by subsection (1).
(3) Nothing in this section limits or affects any powers, duties or
functions that are conferred or imposed by this Act with respect to
the suppression of riots.
Use Of Force In Cases Involving Drunks
(Basically, one can use force against a drunk for doing something that would be a crime if they weren't drunk, even if being drunk deprives the drunk of the necessary intent to commit that crime.)
33.1 (1) A person who, by reason of self-induced extreme intoxication, lacks the general intent or voluntariness ordinarily required to
commit an offence referred to in subsection (3), nonetheless commits
the offence if
(a) all the other elements of the offence are present; and
(b) before they were in a state of extreme intoxication, they departed
markedly from the standard of care expected of a reasonable person in
the circumstances with respect to the consumption of intoxicating
substances.
(2) For the purposes of determining whether the person departed
markedly from the standard of care, the court must consider the
objective foreseeability of the risk that the consumption of the
intoxicating substances could cause extreme intoxication and lead the
person to harm another person. The court must, in making the
determination, also consider all relevant circumstances, including
anything that the person did to avoid the risk.
(3) This section applies in respect of an offence under this Act or
any other Act of Parliament that includes as an element an assault or
any other interference or threat of interference by a person with the
bodily integrity of another person.
(4) In this section, extreme intoxication means intoxication that
renders a person unaware of, or incapable of consciously controlling,
their behaviour.
Use Of Force In Defense Of Persons
34 (1) A person is not guilty of an offence if
(a) they believe on reasonable grounds that force is being used
against them or another person or that a threat of force is being made
against them or another person;
(b) the act that constitutes the offence is committed for the purpose
of defending or protecting themselves or the other person from that
use or threat of force; and
(c) the act committed is reasonable in the circumstances.
(2) In determining whether the act committed is reasonable in the
circumstances, the court shall consider the relevant circumstances of
the person, the other parties and the act, including, but not limited
to, the following factors:
(a) the nature of the force or threat;
(b) the extent to which the use of force was imminent and whether
there were other means available to respond to the potential use of
force;
(c) the person’s role in the incident;
(d) whether any party to the incident used or threatened to use a
weapon;
(e) the size, age, gender and physical capabilities of the parties to
the incident;
(f) the nature, duration and history of any relationship between the
parties to the incident, including any prior use or threat of force
and the nature of that force or threat;
(f.1) any history of interaction or communication between the parties
to the incident;
(g) the nature and proportionality of the person’s response to the use
or threat of force; and
(h) whether the act committed was in response to a use or threat of
force that the person knew was lawful.
(3) Subsection (1) does not apply if the force is used or threatened
by another person for the purpose of doing something that they are
required or authorized by law to do in the administration or
enforcement of the law, unless the person who commits the act that
constitutes the offence believes on reasonable grounds that the other
person is acting unlawfully.
Use Of Force To Defend Property
35 (1) A person is not guilty of an offence if
(a) they either believe on reasonable grounds that they are in
peaceable possession of property or are acting under the authority of,
or lawfully assisting, a person whom they believe on reasonable
grounds is in peaceable possession of property;
(b) they believe on reasonable grounds that another person
(i) is about to enter, is entering or has entered the property without
being entitled by law to do so,
(ii) is about to take the property, is doing so or has just done so,
or
(iii) is about to damage or destroy the property, or make it
inoperative, or is doing so;
(c) the act that constitutes the offence is committed for the purpose
of
(i) preventing the other person from entering the property, or
removing that person from the property, or
(ii) preventing the other person from taking, damaging or destroying
the property or from making it inoperative, or retaking the property
from that person; and
(d) the act committed is reasonable in the circumstances.
(2) Subsection (1) does not apply if the person who believes on
reasonable grounds that they are, or who is believed on reasonable
grounds to be, in peaceable possession of the property does not have a
claim of right to it and the other person is entitled to its
possession by law.
(3) Subsection (1) does not apply if the other person is doing
something that they are required or authorized by law to do in the
administration or enforcement of the law, unless the person who
commits the act that constitutes the offence believes on reasonable
grounds that the other person is acting unlawfully.
Discipline of Children
43 Every schoolteacher, parent or person standing in the place of a
parent is justified in using force by way of correction toward a pupil
or child, as the case may be, who is under his care, if the force does
not exceed what is reasonable under the circumstances.
Use Of Force In Surgery
45 Every one is protected from criminal responsibility for performing
a surgical operation on any person for the benefit of that person if
(a) the operation is performed with reasonable care and skill; and
(b) it is reasonable to perform the operation, having regard to the
state of health of the person at the time the operation is performed
and to all the circumstances of the case.
Most of the scenarios in the question are clearly covered above, and these defenses also eliminate civil liability.
Is it legal to use physical force in the event of an emergency, for
example if you shove someone out of the way of a car and they end up
falling and breaking their ankle, can you get sued?
This is almost surely legal, even though Section 34 of the Canadian Criminal Code would have to be twisted slightly in interpretation to cover this scenario. Section 34 doesn't state that the use or threat of use of physical force has to be a crime, or even that it has to be used against the person who is the source of the threat or use of force.
Canadian law would avoid an absurd interpretation in this circumstance.
