1. well, quite simply, the rules are defined in the files... there are 2 seperate types, and in order to be sure, you would have to look through the data files, but generally, ships and structures and superweapons require the labs that you researched the tech with, however, ablities (excluding superweapons and RA) and passive effects stick around if the labs die.

2. well, you can only get diplo to 10 without envoyes... and then for every envoy on a different planet the limit is raised by 1.5... so inorder to get a rating of 17.5 with your ally (to get the endgame pacts) your ally needs 5 planets, and you need at least one envoy on each of them.

3&4: broadcast centers spread culture (the colored lines) if your colored lines are touching your planet, your planet gets a maximun of 10% income boost.  if your culture is passing through (not just touching, but completly enveloping) an enemy planet, thier allegiance will slowly go to 0, sapping thier income, and eventually causing the planet to revolt.  This works, but it takes longer to kill a homeworld this way than bombarding the same homeworld with a single capital ship.

5. like what you should get first? there is alot of thought on that... but the best thing to do is to get some replays of experianced players and see what they research.  alot of players dont research much untill they get 250 fleet supply maxed out.

6. diplomacy includes entrenchment... thats why you can build starbases in diplomacy, but cant build envoy cruisers in entrenchment.

7. the number goes down when ships and buildings of the target race are destroyed, and the bounty is awwarded to the destroying player (or, in case of rebels or pirates, is lost) 

8. yes, i believe the limit is 150.

9. refineries are wierd.... and there are threads in this forum explaining them.  heres a good thread, about 10 threads below this one https://forums.sinsofasolarempire.com/381433