Can a couple get married at the park?

If it is just you two and the pastor you wont need a permit. Anything over that you'll need a permit to rent part of the park out.

Ask Parks a Rec dept

Yes, but to have a gathering of people (like 10+) you will technically need a permit. I also believe you can rent that half-dome there (as I've seen people have parties) but I'm not sure who to contact

I don't see why not. Just have the priest, father or who ever is going to marry u meet u at the park.

I don't see why not. You might have to get a permit though.