I can answer a few of these.
4. Is there a way to continue playing the game after you've won?
Nope. You can delay winning indefinitely with a few tricks, but once you win it's over.
7. My ships can move two parsecs by default, but in the ship designer it says they should be moving only one. In Dread Lords ships are moving one pc by default. Where does this bonus come from in TA?
In TA most civs have a base speed of 2 instead of 1. Probably the ship designer stats didn't get updated properly.
11. It seems to me that ships' defenses regenerate after every turn. If so, then if two ships with little firepower but humongous defenses fight each other, how will the battle be resolved if neither can damage the other?
The infamous tie rule. After 50 rounds of combat, if neither side has been destroyed, the ships are compared and the stronger ship instantly wins.
12. What exactly can the minor races do? I've seen them build starbases and trade, but will they ever colonize? I think it would be great if they could become major races, be admitted to United Planets, etc.
They rarely colonize. Even if they gain many planets they can't become majors, and I've seen a minor own half the galaxy after a few surrenders. They have extremely high base stats, so giving them a large tech base and manufaturing capability can give a pretty stiff threat.
14. Is it a bug that you can't purchase starbases and starships from minor races?
We could prior to TA, which makes me think it's intentional.
15. Can you culturally annex a minor race's only planet? What about major races' homeworlds?
Minors are immune to influence, but they don't generate it either. That means their asteroid mines are immune to flipping, too. For majors, sure. Everything is game, unless they build the structure that prevents it, and that only protects one planet per civ.
16. When I establish a starbase, it says something about my logistics ability, yet I can establish more starbases then my current logistics. So what do logistics have to do with starbases? And btw, does the game ask you like three times when you are attempting to establish a resource starbase?
As you build more starbases, the cost to build each new base goes up. Your logistics ability delays the onset of this cost. Example: with logistics 6, the first 4 bases are free, then you pay a few bc for the first "extra" base, then a few dozen bc for the second, maybe 70 for the third, etc. Logistics 60 gets your the first 12 free, then you start paying. NOTE: I pulled the numbers out of my ass to demonstrate the point. Don't trust the numbers, it's the concept that's important.
Don't know what you mean about the game asking for mining bases.
17. What is the maintenance cost for starbases?
I believe it starts at 5bc and increases as you add modules.
18. Is there any way you can prevent the AI from establishing starbases in your territory, and can the AI prevent you from doing the same?
There might be a UP resolution that does that, but otherwise no. I know there's a UP resolution that taxes starbases in other people's territory, I just don't remember if there's one that prevents them entirely.
19. Starbases cannot defect, right?
20. If you leave United Planets, will the AI players still hold meetings and get benefits from passed resolutions?
I believe so, yes. Although I know they DON'T have meetings before you join.
21. The manual says that with high enough espionage value, you can predict what resolutions will be voted upon on the next UP meeting. Details?
Manual is wrong. AFAIK this has never been possible.
22. Sometimes your espionage data tells you that a certain ship is moving to a certain parsec. What is an easy way to locate a parsec with specific oordinates?
Usually when you see that there is a colored bar leading away from the ship, indicating it's autopilot path. Follow that to it's endpoint. To find a random coordinate, select one of your ships that has run out of moves for the turn, then play with its autopilot. Select a destination, see the coordinates, repeat until you find what you're looking for. The zero is the bottom corner, and numbers increase as you travel up and right. Sorry, no real easy way that I know of.
23. What can you do with uninhabited planets except blowing them up with a terror star?
Not much. Occasionally there are mega events that will turn all uninhabitable worlds in an area to habitable, or a new minor civ will show up and inhabit one, bot otherwise they are not much but minor terrain features.