After I've upgraded to Snow Leopard and Xcode 3.2, everything was screwed up. It took a while for me to figure out the whole evil was that my old Xcode installation was not really "updated", but replaced. So just everything was gone. All SDKs, Settings, everything.
So Code Sense did not work because of no SDK available, and all the other problems mentioned also just appeared because of that. So now, after re-installing all SDK's, Xcode seems to work fine. Well, almost: Simulator 2.2.1 is gone, which feels more like a punishment for upgrading fast to SL.
After all I decided to re-edit my question to prevent irritations. However, here in short what problems I had, so the answers still match:
1) The font was totally different
2) New Xcode didn't autocomplete CGRectMake and provided no parameter info, for instance. That was because of all missing SDK's and my wrong believe that it was an "upgrade" rather than a whole new replace.
3) New Xcode didn't highlight same symbols in scope. Same problem cause like above.
4) New Xcode never autocompleted anything. Same problem cause like above.
Off topic, but I feel everyone in the world must know: The new Quicktime Player sucks. They removed all important controls like speed and sound tuning, which was always welcome on bad video trainings. Hopefully, they will add those important features again soon.