Hey there, welcome to the forums.
1) Supply: No, continuous lines are not necessary. Every Command Station provides supply to the planet it is on and all adjacent planets. As a rule of thumb, mobile military ships do not require supply, all stationary structures do and mobile non-military ships are the odds ones out and may or may not require it.
Note that Supply does not prevent mobile ships that 'Require Supply' from moving into a system that lacks supply, but all they will be able to do in that system is move.
2) Stars are pretty much background only. Thematically you are fighting in the part of the system that has the warp points, not near the star for that system. Add in a whole bunch of game-engine reasons and I don't think this is something we will ever see.
3) Carry over I'm guessing? If you call something a nuke you know it blows things up. If you call it 'Sciency Fictiony Weapon of Doomy-Doom' you don't get what it does right away and have to read the description. Same reason 'Scouts' and 'Fighters' carried over, they could have been called 'drones' and 'snub-ships' but those don't have that immediate role recognition.
4) 2 AIs are to give variety. The AI type has a
huge impact on how the game goes and the two AI types mix things up a bit in any given game. Fighting against a Fortress Baron/Tank is pretty much a totally different game then fighting a Speed Racer/Stealth Master pairing.
D.