"I do not cook on Fridays."

"To cook" is either "yemek pişirmek" or "yemek yapmak." It just simply must be there :)

You can't use -de or -da with days

İt's uncommon. And it even specifically means on Friday's prayer

Yemek pişirmek is more common than just pisirmek. But your said isn't wrong too.

That means on Friday, but it is saying on Fridays

We never say cuma gün. It sounds like ,cuma is an adjective. We say cuma günü but when you say that it is just for one day. Cuma günleri is a general expression-for all fridays