I wonder if parallel parking with trailer is on the driving test.
No it isn't. The only special exercise I need to perform for the driving test is reversing around a corner to the left. It includes stopping, getting out of the vehicle to lock the overrun brake and asking the driving instructor to get out of the vehicle and warn you of other vehicles. He is not allowed to signal if you're turning wrong, only to warn you if a vehicle turns up.
As for the mass/weight discussion, well weight was the first word that came to my mind, and GVW is what I found in a dictionary. The German term for that is "zulässige Gesamtmasse" -> "zGM".
By the way, Welu: Congratulations!
The problem is that I had to register at the local "DMV" equivalent. If I'd move I'm not sure if I could still do it with them. If I'd need to register again than I'd have to pay the fee again as well, which was somewhere over 100€. Also I'd definitely need to pay the registration fee for the new driving school which is in the same ballpark cost-wise.
Bit more detail about the German/European system (afaik it has been standardised in the whole EU now):
We have many more classes of licenses. Class B is the most common.
Class A in general is for Motorcycles. There are the classes AM for Mopeds (Two-wheel vehicles or three-wheel vehicles with a maximum design speed of not more than 45 km/h and with a cylinder capacity not exceeding 50 cubic centimetres.), A1, A2 and A for motorcycles (with different restrictions of power and driver's age). Then we have Class B, with the trailer extensions BE and B96, where B96 is somewhere in the middle of B and BE (max 4.25t GVM). Then there is Class C, which is for trucks. Class C1 is for small trucks with a GVM of up to 7.5t. Class C1E is for pulling trailers with C1 vehicles. Class C is for large trucks with a GVM of over 3.5t. No restriction on the GVM, as long as the vehicle doesn't have more than 8 seats plus driver. CE is for trailers again. Class D1 are buses with up to 16+1 seats, Class D is unlimited. D1E and DE are once again the trailer extensions.
Class B (the ordinary car license) contains the Moped license, Class AM.