If one of my components breaks, are there replacement parts? My bike was purchased in 1989. It has 7-speed cassette and index shifters on the down tube.

You may want to look on Ebay for 600 parts. Just be careful when reading the description and make sure there are some pictures of the item up for auction. You could always check with a few LBS in your area to see if they have any 600 stuff laying around, you never know they may sell it to you cheaper then on Ebay.