Sounds to me like there is a problem with the freewheel/freehub. This may be fixed by oiling it, but if not I think it would need to be replaced.
If it were me, I'd go as far as I could until I didn't have the right tool (or a close enough tool ) to keep going then throw in the towel and take it to a specialist....If you've got the time, space, and enough tools, it could be a fun activity. Go slow, don't force anything, take pictures so you can check the sequence for reassembly.
You read my mind, but it’s just a cheesy bike, and by the time if I could take it to a specialist the cost for the repair is going to be close enough to just getting him a new bike, which he should have, JR
It's just like student doctors digging up a corpse to learn on...