You ought to regrease such an old bike because the grease can dry out.

Try oiling the hub if it's a three speed. If it's a five, six, or 12 speed, the rear axle could be shot. See if you can move the rear rim from side to side relative to the frame without spinning the wheel; i.e. see if the wheel is a little loose on the axle.

You need to be careful with tire pressure because the rims don't have a little ridge inside them to hold the bead of the tire like modern rims. You can get new tires from Amazon if you need them. It should be fine to use a standard 26X1-3/8 tube.

Harriscyclery.net has aluminum EA3 rims but it will still be a heavy bike. The frame was welded from 1010 steel sheet metal. Electroforged Schwinns are just heavy bikes. I'd say leave the heavy classic alone and get something else for your performance bike.