Well obviously I don' know for sure, but I'm pretty confident in my answers to some of those questions.
1 how much is the max cost of a RS in a give tier (if one exists)?
2 what RS does the AI try to get first, what second, and so on?
3 Which entities must not have any prerequisite?
4 When is it possible (if ever) to use more than 1 (max 2) prerequisites?
5 How comes the same RS used for example in the diplomacy 1.32 Tech Military tree does not get researched in a modded tree even though it has no prerequisite?
6 are RS's bound to specific trees/blocks?
7 Are there research subjects that are mandatory for the AI/the game to work?
8 Can I give some direction to the AI for it to research in a predefined order?
9 What is the use of the RS property "priority"? When needs it be 1, when 0?
1. None, though if its too high obviously the AI may never research it.
2. Depends on many things, including the AI type, but in general it will go for things that unlock ships/buildings just like human players. Beyond that I'm really not sure, though research AIs will obviously spend more resources getting all the techs.
3. Colonies are the big one, both frigate and capital. Scouts I think are also required, and probably a couple of others.
4. I'm pretty sure its possible for anything.
5. Not sure what you mean here, as in the AI won't research it or it won't appear.
6. Nope, you can move them at will.
7. Just fleet supply and capitalships, though if you make everything available at tier 0 you technically don't have to research it.
8./9. Not really beyond the AI types (defensive will try to get mines, starbases earlier etc.). You can try adjusting the priority but there has been no conclusive proof that it does anything.