Hi Airtight
I don't know anything about the social welfare requirements.
But I'm sure if your wife goes with you to the local social welfare office they will explain everything to you.
My advice relates to the language issue.
We moved to France last year and we both speak reasonable french.
My advice to is get a job, any job, even volunteer somewhere to get your german off the ground. It really really really fast tracks things.
I am a stay at home mom and my french hasn't improved considerably since I got here... But a few years ago (14) I started from scratch in a new country with a new language and had to listen to it/speak it every day....by the end of the year I was verbally fluent. So get a job, even a non paying one. (I do volunteer with the school alot and it does help)
Good luck.