Hi everyone!
Welcome to the jungle!
1. Is there a big difference between min 10 and 20? Is this only about "filling" more the room. Perpendicular seems to be very satisfied with the min 10 and even implying that they could sound better because of that crossover-thing (wich I don't understand...) My girlfriend likes the small design of the min 10. I'm a little bit worry that my room is too big...
Perpendicular will chime in, I'm sure, but perhaps I can give you some perspective in the meantime...
The speaker drivers used in the Min series are only 2.25", so bear that in mind when deciding. Cambridge Audio has done a remarkable job with the Min's, but brilliant engineering can only mitigate so much - there are certain immutable laws of physics that must be considered as well.
The Min 20 is not a traditional 2 way speaker, it's 1.5 instead. That essentially means one of the drivers is a "tweeter", but both drivers are being used for the midrange. The latter range is very critical so CA decided to emphasize it, which is not a bad strategy. In order to make that work though a crossover must be used, but my buddy Jeff (Perpendicular) absolutely hates those things.

Both are diminutive of proportion; the Min 10 is tiny, and the Min 20 very small, so I suspect either would be OK with your girlfriend.
2. What about 3 min20 and 2 min10. I read about it but somebody actually tried it?
Min 20's for the front 3 channels, and 10's for the rears, would be the minimum (no pun intended) that I would use, given your circumstances. At the very least I'd use a 20 for the center.
3. For the sub, I want to go with the X300. With the opening at the back of the room, would the x500 be a wiser choice?
Of those two I think you'd probably be better off with the x500 than the x300, but it depends upon what you're looking to achieve. HT needs a pretty powerful subwoofer, so it's advisable to make sure that's potent.
FWIW... while Cambridge Audio does make some fine products, I think they're subwoofers are not very price competitive. There are other companies that make excellent products, but cost far less. One example would be the Emotiva
Ultra 12. It's on clearance because it's being discontinued, but I can personally attest to what an excellent value that is. It might not go as low as you'd like for HT though, but that's just one example of what else is available.
5. Finally, do you have a thread or internet site about ABC's of HT to recommand? Don't want to loose myself in google!!!
A couple of threads you might find some value in are:
A Guide To SubwoofersSpeakers 101A Guide To CablesHome Theater Virgins