Got severance, how does it affect benefits? - any advice?

I was offered severance of 3 weeks after being let go as a teaching assistant and I am unsure how it affects benefits. I have read a lot of threads here and could not find my exact situation. I also wonder about the job-search requirement. How did your state treat it?

Before signing, I asked a friend who is a lawyer to look at the agreement. It was a short conversation and worth it.