Is there wheelchair access to the picnic tables / wheelchair access in general?

Yes

Yes, there is wheelchair access to some of the picnic tables, the restrooms and the tennis court. Be careful, however; there is construction going on there, and some of the picnic tables are currently inaccessible. The City of Melbourne Parks Dept. is rebuilding the boat ramp.

yes it's a pretty flat surface

It's flat but not necessarily paved