Your last example - an indirect command or request - is quite common in formal contexts, such as minutes of meetings, and even in speech for some speakers, though many would say "that he files".
The other examples are much rarer: they are archaic, and few people would use them except in special registers. But anywhere you could use "If I be", you could equally use "If he jump".
We agreed that, when xyz happens, we would do abc
This sentence does not make sense to me. If ‘happens’ is present tense, xyz clearly is still in the future (or is a general statement, ‘when’ meaning in effect ‘whenever’). Therefore, ‘do’ should also be in the future (or present) tense, rather than in the conditional mood:
We agreed that, when xyz happens, we will do abc
We agreed that, when xyz happens, we do abc
Having ‘happens’ in the present, but ‘do’ in the conditional creates an impossible time line, and the sentence collapses semantically. (Although in colloquial language use, I’m sure you’d be quite likely to hear it used)
However, since you say that xyz was future when the agreement was made, but is now past, this is not the proper option to begin with.
We agreed that, when xyz happened, we would do abc
I’m not sure what contingency it is you feel is not expressed here. If you know for a fact that xyz has in fact happened at the time of reporting, there is no contingency to express: it is an at the time future event that is now marked as having actually happened.
In general, I feel the sentence would flow better if the latter two phrases were reversed:
We agreed that we would do abc when xyz happened
But that is a matter of style alone.
As for your last question, I am not aware of any particular grammatical term for the interaction between such constructions, but I’m sure someone has coined one somewhere.
Best Answer
We can use the present for scheduled events in the near future. However, we don't use the present at the time we are scheduling the events.
The sentence
sounds to me like I am informing the listener of the arrangement. In this situation I would use will pick you up rather picks you up, I think because I don't consider the event to have been scheduled until the listener is informed.
On the other hand, if the listener already knows about the schedule, and we are just confirming the arrangements, I would use picks you up.
And in situations like the concert starts at 7:00, I would use the present tense regardless of whether the listener knows already, because this event is scheduled even before the listener is informed.