Yes, glad you're enjoying it!
To add to Keith's comments:
1. To prevent the AI from rebuilding turrets from remains, just bring in a cleanup drone (or three) of your own to deal with that. Or, once you kill their command station, then of course that automatically prevents them from rebuilding, as you noted.
2. If the planet is weaker than your defenses are, then popping the command station early is a great idea, because it can let you fight on your turf with your turrets, rather than on their turf with their turrets and ongoing reinforcements. But, this can backfire and get you killed if you are not careful with it, so often just going around and picking off the various guard posts before taking out the command station is the best course. Once you kill the guard post and the mobile ships guarding it, you can ignore the turrets if they are not n range of hurting you on an ongoing basis; then come back and clean up those later, after the command station is dead.
3. Sometimes it is nice to create a "dead zone" that is a buffer between you and the AI, which would be when you kick the AI off the planet but don't build a command station of your own. The majority of the time, though, you will probably want to build a command station because you've "paid" for that planet already in terms of time, AI Progress, your resource expenditure, etc. So best to capture it and let it start generating more resources for you, if you can use them and it's not going to create a weak spot in your defenses or anything.
4. To clarify keith's response to your #2 question, supply does not have to be all interconnected as one network. So when you go out of supply and kill an enemy's command station, and then bring a colony ship over in a transport (usually colony ships cannot make it there without the transport if it is out of supply, due to enemy fire), then you can take the planet for yourself. Having a command station on a planet gives supply to that planet and all the adjacent planets, which then can give you a pretty powerful forward base at way less AIP cost.
Good luck!