Hey, that could be a nice bike. Personally, I'd clean up all the original components and put them back on it. But then I don't like fixies. But you should do what will make you happy. As for rust, that headset will clean up with a can of Nev'r Dull (any auto parts store) and your fingernail or a plastic knife. Thin rust like that on chrome is almost always fixable. Contrary to what you read elsewhere, don't take steel wool to chrome or aluminum parts. You don't need it and it does more damage than good. Use some Nev'r Dull on the rust, rub it well, then use your fingernail or the plastic knife to scrape it abck. Nev'r Dull will make aluminum shine like a mirror. For somewhat pitted non-anodized, aluminum bits, 1500 or 1000 grit wet sand paper followed by... Nev'r Dull, will shine up just about anything. Be very careful with the sand paper on detailed edges.

Karl