Covered storage for my van during hot summer or uncovered?

Put a skylight in the covered parking over the panel(s), as all you need for power is likely to be to keep the batteries full, and maybe a fan running?

I think I would find a way to either do the above, run a cord, or get a small portable solar panel before I would leave it out in the hot sun all the time. Everything degrades in the sun, for the most part.

No, no, no. The sun is your friend and helps protect your van from....ah...moonlight.