Clean keycaps with denture tablets, move up to soap and water with a sponge if needed, flitz polish as a last resort (it will wear the caps down, other two are perfectly safe). Caps are doubleshot iirc so no risk of wearing off the legends.

Retrobrite at your own peril. I do not advise. That said, only ABS plastic goes yellow with age, so the same techniques for retrobriting will work on both caps and case.

Cleaning the spring with conventional rust removers is up to you but the springs will rust again so I say to leave the rust on to protect against future rust. Oiling the springs would help though.