Can you have a birthday party there and how much would it be to rent a covered area

Call the ranger station. There are areas that can be reserved and some that are on a first come basis.

I don't think so.

Check the On-line registration for that park.

Look for reservations online. There was a wedding going when I went, so I assume there must be some kind of venue service.

I think it's on a first come first serve basis I'm not sure