For the CO alarm, there's no real need to get an RV-specific unit. A (battery-powered) household one will do just as well and is a lot less expensive.
The microwave could be the microwave itself, or the wiring to the microwave outlet being loose/high resistance. To test, you'd need to pull the microwave out to get access to its outlet, and watch the voltage at the outlet when you start it up. If the voltage droops when it is cooking, you have a wiring problem, probably a bad connection at either the outlet or the electrical panel. Assuming it's the typical insulation displacement sort of RV outlet, I'd be tempted to replace it with a good quality household one (in a box); the RV type aren't really ideal for high current applications.
If it's the microwave, it's probably not cost effective to repair unless it's a very nice microwave or specialized in some way or you're skilled at such repairs. Microwaves can be quite dangerous to work on if you're not familiar with them; the magnetron power supply has an output in the kilovolt range and can supply a significant amount of current, making it potentially lethal.
I agree with the comments about sealing. Inspect all the caulking and replace/cover over any that looks at all questionable. For the roof, Dicor self-leveling lap joint compound is the standard and works quite well. Avoid silicone entirely.
