Is there an actual park anywhere near the pavilion? One with slides or a swing

Yes

Yes there is and the concession stand will be opening soon.

Yes and it's really nice!! Right I front of the water to the right of the pavilion

It's on the East end of the Park.

Yes, at the East end of the park

There's a park just East of the Aquatorium (the old Gary Bathhouse) for the kids.

Yes there is. It's a beautiful park.