If your company has a "Betriebsrat" you should speak with them, and they'll be able to answer your questions.
I was made redundant last year. Here are a couple of things from my experience:
1. I don't think they can stop you looking for another job during your notice period.
2. If you do find another job, you may be able to leave before the end of the notice period by signing an "Aufhebungsvertrag". Don't sign this, however, without having it checked by your lawyer and/or the Betriebsrat. Make sure that by signing it you don't invalidate your claim to any compensation.
3. Compensation in my case was based on age, length of service, salary, marital status and number of dependents. The formula used to calculate it was argued between the Betriebsrat and the management for ages.
4. If you intend to claim any government benefits, you have to sign up within a certain period of time after your notice was given. Check the TT
unemployment benefits info page.