If I want to do a family picnic and don't want to rent a shelter at a park can I just bring my tables and chairs at no cost or do I still pay

Yes easy to set up under a tree

Probably yes

How much is it if I wanted to rent a picnic area?

I personally never done it but I've seen it done I believe it could be done

Yeppers no problem , great place for a family picnic

Yes you can. It's a park anyone can have a party there