Are the grills normally pretty clean within the park?

Agreed, they are generally pretty clean but, it's better to be prepared than to be caught off guard. And of course, they are charcoal grills as opposed to propane.

Yes, the whole park is well maintained.

Your fire ring has grill bars over half way, on a lid you can raise to put more wood into. Very few standing grills on camp site. There are picnic areas with standing grills.

Yes

I would clean the grill if in doubt.

I agree with Mark. Better to come prepared to clean or use a foil pan with holes poked in the bottom. ;)

For the most part, however I usually take a grill brush.