You are right, first problem was in front of the computer.

The group trick couldn't solve the second one.
Interesting is, that after adding contacts to the group and doing other things more contacts started to sync. Still less than 20% of the approximately 135 belonging "Meine Kontakte" the standart group in Gmail. Surprisingly more contacts are synced with -a account than with -a account+testgroup where testgroup is the group I added all my contacts too. I also wont work adding 3 important contacts to a group and using that group. No one of them which wasn't synced before gets synced that way.

Explanation of my contacts setup? Hm, what can I say. I have 135 Contacts+ 332 under "Weitere" (which means additional, the group at the very bottom)
The 135 contacs belong to different groups, some to multiple ones, some to none.
The information which belongs to each contact varies widely. From a single mail without a name to name+multiple mail addresses+multiple phone numbers+address+notes

I know this is hard to debug without access to the problem set. The only hint is the message which appears at the end of each sync:
'NoneType' object has no attribute 'given_name'