In general, you can file a complaint asserting any cause of action whatsoever against a defendant, even if they are unrelated, in the same case, and if you don't, you risk having the claims that you do not file barred by the doctrine of res judicata, which bars new lawsuits between the same parties not only over all claims that were actually asserted and litigated between two parties in a lawsuit, but also all claims that could have been asserted and litigated between the parties, but were not actually litigated.
In American civil procedure, leave to amend your complaint is generally speaking, freely granted and discovery of new information would ordinarily constitute good cause to amend your complaint. But, there is also usually some sort of case management order that sets a deadline for amendments to a complaint and requires a much higher showing of good cause to amend it after that deadline.
In the federal rules of civil procedure, amendment per se is governed by FRCP 15, and deadlines set by the court for taking procedural steps is governed by FRCP 16. See also FRCP 18(a) which states that a party may include as many alternative or independent claims, legal or equitable as he has against an opposing party and FRCP 18(b) that claims that are conditional on each other (like breach of contract and a fraudulent conveyance claim to seize assets transferred improperly by the breach of contract defendant if breach of contract liability is established) may also be joint in one complaint.
Your second question pertains to joinder which in the federal rules is governed mostly by FRCP 19 (mandatory joinder), FRCP 20 (permissive joinder), FRCP 21 (misjoinder) and to a lesser extent in special cases by FRCP 22-25 covering special cases not applicable to your question.
FRCP 19 says you must join parties necessary to provide complete relief on the claims as between the parties named. FRCP 20 allows for permissive joinder when there is liability that is joint, alternate, or arises out of the same events if there is fact and law common to them. FRCP 21 states that if too many parties are named or not enough are names that a joinder or severance motion, rather than a motion to dismiss is the proper solution.
The scenarios identified involve permissive joinder, so they can be joined in the same action, but they don't have to be joined, in each of those cases.
Joinder motions should be granted whenever timely made and appropriate, so long as this is consistent with FRCP 15 which grants leave to amend liberally. So, the only real barrier to joinder in the second scenario is any deadline for amendment of complaints or joinder established by FRCP 16. Prior to the deadline, leave to amend to join these parties would be freely given. After the deadline you would have to show that there was a very good reason to do so, because the parties while they can be permissively joined, are not necessary parties and could also be sued in a separate action. This said, there is some argument that in the case of contributory liability that joinder is really necessary per FRCP 19, and that allowing this joinder is therefore appropriate even after the usual deadline and even if it leads to delays.
In Colorado practice, to avoid these kinds of situations, contributory liability can only be asserted with respect to a non-party if that party is designated by a defendant as a "non-party at fault" in a pleading that has to be filed in a time frame that would usually make it possible to join that non-party at fault to the action to avoid an "empty chair" to whom liability could be assigned in this case before the deadline for joinder expires.
once I have a party in a civil action, are there any rules that
constrain my ability to unleash a litany of unrelated but substantial
complaints against that party?
There is really only one exception although its subtypes are myriad and impossible to list completely.
If you sue someone in a special statutory proceeding that is limited by statute to one narrow issue (e.g. a suit to enforce a records request from a corporation by a shareholder, or an eminent domain condemnation proceeding by a governmental body against a landowner), claims unrelated to that one narrow issue that exist between the parties may not be asserted (and those claims are not barred from being brought separately by the doctrine of res judicata).