Those short fenders are totally useless to keep water off, but they look good on a bike of that age.

My experience with older bikes is that the grease in the bearings is dried out or non-existent, so take care of that before riding very much. Wheels, crank, headset (where the fork pivots), will all need attention. New cable housing with lining will improve braking and shifting. Also new brake pads.

Cheap American 10 speeds usually had 26x1 3/8 tires, which are available, but there is not a lot to choose from. They are NOT the same as mountain bike 26 inch tires. 26x1 3/8 is ISO 590, mountain bike 26 inch is ISO 559. Take a wheel to the shop to make sure you get the right ones.