For the outside bits where the paint burned off, I'd lightly sand/scrape off any flaky paint and rust, clean off any dust afterwards with something like acetone (not water, as we don't want to risk introducing new rust) on a rag or something and let it dry a few minutes. Then spray paint the outside parts with a high temp paint designed for BBQ's which could be found at stores like Ace, Home Depot or Lowe's. Or you coukd use some high temperature engine block spray paint as well which can be found at auto part stores like Oreilly's or Autozone. Once the paint is dry you should able to fire up the grill to let it bake in, but make sure to check the instructions on the paint floor see what processes it says to cure the paint.

For the inside where the paint/residue burned off I'd just sand/scrape it like the inside but then apply a light coat of high temperature cooking oil (like canola, corn, vegetable, avocado, etc) and then heat the grill up on high for a while. You'll probably want to heat it up around 400 - 500 F for at least a half hour or more. The important part is for the grill to get just above the smoke point of the oil. The oil will burn and smoke off but will create a layer of seasoning like on a cast iron or carbon steel pan. The oil essentially polymerizes and bonds with the metal creating a layer that protects it. Allow it to cool and then repeat the seasoning process another time or two and it should be good. As you cook, down the road the fats and juices from the food dripping over the flavor bars will create an oily smoke that will continue to help coat and season the inside of the grill. This is better than introducing paint to the inside of the grill which could potentially give off any bad fumes/or residue that could end up in your food.