Sounds like a fun project but it's easy for a big project to consume a person and make 'em pass it on to someone else. Take it slow and plan it out and take one bite of the elephant at a time.
The rust will only get worse. That looks like a simple job for a mig welder or even a flux core if very carefully done. I'd cut out any of the rust and patch it. You want to build on a good foundation.
I'd cut, patch, straighten then touch up. If welding - removing any adjacent flammable or meltable material is critical so that should solve your question of removing stuff.
After welding fill any voids with rust proof paint or wool fat (let the experts chime in here).
As far as the top mechanism - if it gets distorted then everything will be cockeyed. Better to loosen that sucker at minimum so that any dent removal is done just to that spot. You can straighten anything needed on the mechanism separately.
This cat is the best I've seen for body work on youtube.
Edit: one of the original RV owner staples was "12v Side of Life". It's pretty dated by today's standards but it would be useful to check out. I'm sure there are more modern renditions of the info. Fortunately with 12v, nothing is very dangerous if done carefully. Check for bare wire, opens, shorts and make sure batteries are disconnected when you do anything. Learn about various connectors and practice with them before game time.
http://wanderlodgegurus.com/database...0of%20Life.pdf