No bases contribute points towards controlling the planet.
You can take over a city by killing all the NPC guards and holding it until the countdown expires, I think that's about a half hour but I'm not completely sure on that.
Some cities are always one faction, like Bestine will always be Imperial and Anchorhead will always be Rebel. But the other cities can have their faction changed.
When you attack the city guards they will send out a distress call and in a few minuits some very difficult reinforcements will show up to defend the city. If you can take those out and deal with any players who happen to show up you should be able to take the city.