It sounds like things are going ok.
Yes, you can build starbases in other races territory, but they usually don't like it.

I'm suprised no one else has built on the that resource yet as the AI tends build on them quickly.
As you get upgraded factorys, markets and so on tech, your existing ones should get updated automatically. No need to replace them.
Start woking on building up your military, which may involve some more techs. If you wait to long without any defenses, the AI will take advantage of you. Besides, you want to go visiting them with troop transports anyway, don't you?
You can also start building influence starbases near other race's planets. The long term goal of that would be to get those planets to rebel agains thier current empire and switch over to yours.
I only build starports on planets that have reasonable manufacturing capacity. No need to waist the terrain tile to build one if it can't build ships in a reasonable amount of time.
Keep playing, keep experimenting, and keep having fun!
Tony