melted"! Sounds like the P.O. hit it with a can of rustoleum before selling...
Looks like an original stove- they were all plated steel, and every one I've ever seen shows surface rust after all these many long years. Not much to be done- and believe you me, I've tried. Heat-"proof" paint
will last for a while, but not forever. You'll have to remove the regular paint that's already on it for that to do any good, though. I did recently replace my stove, strictly for cosmetic reasons. The new one came out of a popup and is within an inch of exactly the right size...so they are out there!
Per the yellow flame:
That's an indication of too little air. I'm having a little trouble seeing detail in your pics, but there should
be an air-adjustment slider or screw of some kind near where the burner tubes connect to the gas supply. It looks to me like there's a sort of random mix of adjustments there-?
Another possibility, especially if the trailer's been unused for some time, is spiderwebs/bugs in the burner tubes, which will block air. Removal and blowing out is customary.
All of this presumes that your trailer regulator is working properly...if you used the fridge
and its flame was the normal blue with just a bit of yellow at the tip I think you can rule out regulator malfunction.