You can chip away at border planets that you already have some cultural power over but taking a planet deeper in someone's system is a very hard to do.  This just makes sense to me and is how the game should work.  Think of culture as your supply lines with a ground army, you can't just push deep into someone else's supply line and take a city and expect to hold it without a supply line of your own helping.

That sounds good idea. I will try that! If I could, I would also ban them from trading tech or at least make it very hard for them. Now it feels they all have it as what comes to important things like ship sizes. And not only they trade, but I suspect they also steal mine    That's why I decided to play without inventing the hyperwave radio, but I don't know if it really stops them from stealing. At least the fact that I cannot communicate doesn't seem to stop events where I very much communicate   

There's a game option for that. You can disable Tech Brokering, which means that they can only trade techs that they have researched, not any that they traded for, or you can disable tech trading completely.

I generally find that I need to take the homeworld first. Without it, most of the planets I could take would culture flip back to the original owner. With it, most of their planets will flip to me in time.