How to reduce how much a flat roof heats the house

This is done all the time by insulation contractors. The technique is to drill a series of holes at the top of the wall. They next use a commercial 'blower' that forces insulation into the walls bay. It is a very non-invasive form of insulating because (as you asked) it doesn't necessitate the demolition of existing walls. It is also well with-in a competent DIY-ers capabilities and machines can be rented at most home centers.

First: yes you need to remove all the rust before repainting, or the paint will just flake off as the rust continues.

Next: you need to make sure that there's some "body" left after initial sanding/scraping of rust, or you might as well replace the sheets. You also need to verify that all rust is on the top, i.e. there's no leaking and bottom-side rust (or you'll need to fix the leaks).

Assuming all that went "ok," then sand & scrape all the loose rust off, and do your best to sand off the rest. Paint all exposed areas (with rust pits or not) with a "rust reducer" paint, available at any hardware store. Typically these go on white and cure black; they both reverse the oxidation (rust turned back into iron) and provide a good surface for painting. Then put down whatever color of metal-compatible paint you want.