Work permit restrictions

I recently applied for my freelance work permit in Cologne. Along with my work permit application, I included my "letters from potential employers," all of which were English language schools. I was wondering, in my case, would the freelance permit also allow you to have a small side job that is not related to teaching English? Or, is the work permit job-specific?

Job AND employer specific.

Usually.

I got a freelance work permit in Cologne. Only allows me to work in my specific field.

Another question if I may?

Can non-EU students apply for a freelance visa on top of their student visa?