Woa, that's actually more than one question :-). I'll try to answer as much as I can. For clarity, I split your post into multiple simpler questions.
As to jurisdiction: I'll try to keep my answer general for most European jurisdictions, additionally citing UK law.
Is "hitting back" self-defence?
To quote the definition of self-defence:
A person may use such force as is reasonable in the circumstances in the
prevention of crime, or in effecting or assisting in the lawful arrest of
offenders or suspected offenders or of persons unlawfully at large.
Criminal Law Act 1967, section 3 (1)
As you can see, violence is only self-defence if it is a) to prevent a crime, or b) to assist with a lawful arrest.
So if you just hit back to retaliate, it is not self-defence. However, if you believe the attacker will hit you again, and hit them to prevent this, it is self-defence. Of course, which case applies is something a judge/jury would have to decide, thus the answer "it depends".
Does it make a difference if violence was preceded by provocative actions?
Yes, but only for the person provoking.
In your second example, the violence was preceded by a "heated discussion", possibly involving threats. Self defence is only permissible, as the term implies, to actually defend against a threat. Hitting someone because they annoyed you does not count.
That said, if you are accused of a violent act, the fact that you were provoked will probably count as a mitigating circumstance. However, this will at best reduce your sentence, it will not make something count as self-defence.
Also, in some jurisdictions, if Jill provokes Jack, and Jack then proceeds to hit her, this will (somewhat simplifying) make it more difficult for Jill to later claim self-defence if she hits back. Since she provoked the attack, she is only allowed to defend herself, but not to attack preventively (which would normally be considered self-defence). The idea is that you cannot provoke someone into attacking you, then attack back claiming self-defence.
Does it matter whether the people involved are adults or minors?
As far as I can tell, the right to self-defence does not make distinctions based on age, so with respect to determining whether an act was in self-defence, it would not matter. The law does mention that the force used must be "reasonable", and for a minor accused of violence, a court might apply that criterion more leniently, because for a minor it might be more difficult to judge what is reasonable, but that is just my speculation.