The bit with the bracket that painted you wont be able to do much about. Looks like its been welded at some stage and painted after.
I would mask it up neat and paint it. What colour would depend on the colour of the mower etc.
As for up near the handle. Try washing with detergent and a scotchbrite pad or one of those scrub buds. It should come up pretty fair. You could try polishing after that.
Keep it dry and it should stay good. A bit of WD or similar will help keep the rust away.
If you touch it with sand paper you will have to paint it or it will just rust as you will damage more chrome and expose more metal.
Bob.
