I am sure that these questions have been asked multiple times in here over the years... I just can not find it .
Only mapmaking, please no solutions requiring modding.

1. Is it possible to force an +1 upgrade using triggers somehow? The intention is to have gradually upgrading opponent, preferably all the way up to +5. (I do remember Spellsword preventing an 'forbidden' upgrade even though player could have tech, button and resources for it. It's probably not related... but maybe?)
2. Will any AI upgrade past +3 under any circumstances?
3. Can I lock some tech after the game already started? Let's say I want player to be able to choose between 'commanders sc2 coop style' and want to prevent them from building some units, but I do want them to be able to mind contol and use them as well. Removing tech structures as soon as they build can achieve it, but what if I wanted to disable a Zealot for example? I would also like to prevent mind controlled scvs from building, but be able to repair.
4. Can I give units that normally don't have abilities access to them? Let's say Archon with Psionic Storm?

1. assuming you do not mean starting upgrade level ( which can be set in UMS ), only with EUDs or modding
2. with modding (technically you could bundle a script with EUDs I think?)
3. with modding, not sure about EUDs
4. with modding unless iscript allows it, then also with EUDs

Nothing of this is possible in standard UMS

EUDs are mapping. Do you happen to know what to look for to do this?

EUD Editor>Trigger Editor>Action>SetUpgrade

Thank you Sayoka