Are there open spaces to sunbathe and picnic here? Or is it all trails / creek?

There are tables of the parking lot and more inside the park. At the pump house turn right to get to them.

I would say no. It's a forrest preserve.

The picnic tables are straight back near a tomb looking thing with a bell on it be on the look out though i did see a snake when i went but it wasnt aggressive just passing through you can sit in the water but its mostly shade and you will be thankful for that by the time you get to the cave/waterfall anyways its a small hike up but worth it

There is an area with picnic tables located within the park.