Is the lake pool and grills near each other? Also how early is sudgested for a nice spot? Are these places also near the parking lot?

The pools are a bit of a walking distance along hiking trails. Some of the grills are near the parking lot.

Yes grill's are near to lake n parking lot. You can enjoy grill's with lake view. Availability of grill's depends upon the people visiting that day so if it's long weekend you need to go early in the morning.

Yes yes n sort of..

The grills and tables are near the parking lot and the pool is near the hiking trail

Not all, to parking nearby.