Can you have a cook out there

Yep there are grills

Yes

There are multiple grills provided at the pavilion locations (near the pond and playground areas). Do keep in mind though that if you are planning to go during the weekend the grills are usually occupied during meal hours.

There are places will grills, not sure if all of them require reserving a time with Parks and Recreation. As far as I can recall, the covered areas on the bigger playground do, though I don't believe they have grills though.

Yes the grills are next to a beautiful pond...it also has nice walking trails and a playground