Could also be a stretched out chain, and since you've suggested that it might be the original, it's almost certainly time for a new one.

As for the tires, the lube suggestions are on the money, I usually use keep a jar of water with a squirt of dish soap on hand, and swab it over the bead with a rag or sponge before inflating. Also, be sure your tires say "nn-590" somewhere on the sidewall (where the nn represents some other number.) If there's a 597, you've got the wrong tire.