Does that actually work?

What did you use to glue the styrofoam together?

I remember that pain, but I bought some 16 inch drill bits and stacked and clamped my plywood together and drilled through 5 or 6 sheets at a time.

1. Those joists should be able to hold the weight of the wall with no problem. I recommend using 3/4 inch plywood tho instead of 1/2 inch. Will feel more sturdy.
2. As long as you are going directly into those joists you shouldn’t have any issue mounting monkey bars or other hanging things.

I do not do construction personally, but I did build a home rock wall for the kids and have a 30 degree incline that I can climb and feel secure on