Naugatuck State Forest

There is a brook or river did not see a no swimming sign, I was very clean and looked refreshing for a steamy summer's day dip

There are small spots to park at many of the trail heads and a small lot at the bottom of the mountain next to the rr tracks

Yes

No since I've had DEP up top yelling for catching those nice largies on top lol.. sunrise to sunset my friend

Yes hunting is allowed during approved seasons see ct deep website for zones and appropriate seasons

Yes

There are no paved paths.

No

It's a large area, but I'm not aware of any designated places for that. I'm actually not sure there are any picnic areas in the forest at all.

Coming through Beacon Falls is faster but rougher Naugatuck side is paved depending on which town you came from there is a parking place where the dirt road & pavement meet walk onto the road into the dirt road through the guard rails & on your right will be the waterfall trails 20 25 minute hike on your right right after the guard rails not well maintained!! don't miss it

Some spots have a posted trail. Map. No cost, no staff

It's considered a state park so that would mean no hunting but there is an area on Hunters Mountain that is not state land and I've seen turkey hunters there. You would need a topo map to determine where state land stops.

No pool but several lakes