1) The game has a bug that will allow you to move a TS anywhere you like in one turn. Even from one side of an Immense galaxy to the other. It does, however, seem that most people are completely unaware of this.
2) I am personally of the opinion that Terror Stars should be one-use ships; they should blow up with the star. After that, we can potentially discuss making them more viable in other aspects, but without it, any improvements to them would simply make them overpowered.
3) I can't remember ever being allowed to place multiple constructor modules on a ship, but it's been a while since I've been able to play.
4) The AI does react to your building and using Terror Stars, at least at the higher levels.