Steel requires rust proofing. Just like on you car, there is a thin layer of primer under the top color. When scratched to the base metal, sanding and painting the affected area is necessary.
Sand until the exposed metal is shiny. Depending on the spot, you can use a high grit paper, or wet sand paper with water. You might want to start with 200-300 grit and then maybe 400 or 600. You're working with a small area so you don't want to press hard when sanding.
A good technique to make sanding with paper easier is to fold it a few times to get into tight areas. Folding gives you a stiffer sheet edge and you can work it in crevices. Also wrap an inch or two of paper around a woodend dowel, or even a pencil. A round shape will help you sand the long vertical scratch on the fork without having to sand the whole width of the fork surface. The round shape will only touch the suface in a long thin area instead of a wide area.
Wet sand paper is usually less than a dollar at most hardware stores when bought by the sheet instead of the pack. You shouldn't need more than a sheet or two of each grit. Wet paper last a lot longer than dry. It can also be cleaned/washed.
Use a high percentage alcohol to degrease and remove dust after sanding. Dry thoroughly if wet sanding before using the alcohol.
Then prime, even if it's just dab priming. Allow the primer to dry thouroughly and lightly sand the primer back to where the original paint just shows around the wound. You can also use a high number wet sand paper with water to lightly sand.
Look for a paint match at an auto parts store. Dab the paint on primed areas and let dry. Wet sand with high grit paper to match the original finish. Treat the paint like a regular car. Small amounts of paint polish will give you a good shiny finish with little work. Apply wax and enjoy. Paint like yours should last a long time.
1) Rough sand with shaped paper to get the rust off down to the metal.
2) Wet sand for a finer surface finish.
3) Dry, then degrease with alcohol.
4) Paint with primer.
5) Sand the primer and lightly dust with lint free cloth(cotton ball or pad) and alcohol.
6) Apply matched paint.
7) Wet sand with fine paper.
8) Wash, then polish and wax to shine.
9) Enjoy for years to come.