Install uni trim as a j-channel to receive the panels.

You can order polyiso in a variety of thicknesses. It’s not as moisture resistant as EPS or foams. Batt insulation is ideal for this situation.

You can fabricate your own cleat attachment when you tab the top inside cut. Or use other hidden fastener methods

Poly-iso is a similar insulation as "foam board" with a fire rating and higher r value.

Florida licensed home builder here! It depends on the stair skirting for what you will do with the wall layout.

Bridging the framing with 2x2's between the studs would be the best solution for the base and rail to keep your vertical seams tight. You can also fill between the studs with rigid insulation for support at the seam.

Use counter battens ripped from plywood at the thickness you need for the base and uni-trim.