Can your rank get better when playing in a created server? Can qi go up in a private server?

Nop, your rank wont go up faster by playin in created or official rooms, and your QI will always increase whether you win or lose, in any server, whether created or official.

The only difference is that you gain 10tc per win in official servers.

So you can advance in belt on a private server?

Yes, but farming QI results in perma ban.

Sorry, really hate to bump this but one more (and lol I'm not going to farm, just wondering if i waste games) does win % change also?

Yes. It changes.

And don't farm.

Can Administrators see our IP adress? (out of curiosity, I'm not gonna farm anyway.)

Yep, of course they can see our IP's.