So my questions: Do I get a new empty wallet, when I register at bitcoin.de ?
Or is there a possibility to create one after having registered ?
No, you use their already existing wallets. I'm not sure exactly, but they probably simply assign a deposit adress to your account, and use that in combination with a DB to keep track of your funds.
Every time when I try to login at "bitcoin.de" from my desktop PC,
I have to wait for an E-Mail TAN as a 2. step for the login.
This takes about 20 minutes every time.
I have a windows-smartphone. Is there a possibility to make this login quicker
by using my mobile-phone ?
I'm not sure. I doubt a lot of people here have experience with bitcoin.de, so it might be smarter to contact their support on this matter. (As bitcoin.de does NOT represent bitcoin as a whole, if that was what you were thinking.)
Alternatively, you could download a wallet for your Windows Phone and store your bitcoins on there. It's safer, and probably much faster to access.