Absolutely ditch the old chain. That bike deserves a $14 investment, at the very least
Think 8-speed chain for starters. Any one available will be better than what you have now.
Ditto on getting whatever 22.0 stem you like; the you have is really short, especailly for such a big frame. Are you 6' or better? If so, the bike will probably fit you pretty well. Get some chrome top tube cable clamps to replace those zip ties.
Probably needs new tires, lube in hubs, headset and bottom bracket (if it hasn't been done recently) and possibly cables and housings. Then ride it as it sits; give those Simplex derailleurs a chance, they are fragile with age, but they work pretty well until they break.