Can I use this on rusted door hinges without taking them off? Do I have to paint them afterwards, or will they be okay with the rust removed?

The Loctite Rust Neutralizer is a spray-on-product so removal would be recommended unless protection of all finished surfaces is possible. This product can damage finished surfaces and may cause rust if applied to a non-rusted metal surface. If not painting, 2 coats plus a top coat are required otherwise painting is required. Do not use latex base paints unless a solvent based primer is used beforehand.