The first step is to take everything apart to a bare frame, and since we're going to rebuild the wheels, that means taking apart the wheels as well.
Repair the bent frame:
Recondition a Shimano B-Type Coaster - clean and lube it:
Rebuild the back wheel with the new coaster and the de-rusted original spokes and rim:
Make sure it fits - the coaster hub will need to be adapted to the width of the frame:
With a variety of recycled nuts and washers, I matched the width of the hub with that of the frame, making sure the hub remained centered. I also had to slightly bend the arm of the coaster hub so that it would reach the chainstay.
One of the pedal arms' thread was busted, so I changed the whole crankset with a recycled 1980s Sakae crankset, from which I removed the small chain ring.
I trued both wheels and installed them to make sure they were perfectly centered: