Maybe not for these specific problems, but Black Rustoleum spray paint is your friend on frames. It cleaned it up and painted right over the rust and it sealed it and stayed. I said no prep needed and meant it. I have places on mine five years later that look just fine. AND the paint matched almost exactly with the original color. You have to get down and look close to see any difference.
I now have the "hammered" version for my iron cross front bumper on my Truck that after two years is starting to rust in places. I am experimenting in not too visible places and after six weeks looking good and cannot see any difference. The hammered black is also almost the same color as the "hammered" look on the original powder coat.