How old is he now? Still with mom?
Does he walk out of it? It looks like his weight is pretty good and his issue is likely conformational (not helped by his initial poor care I'm sure)
I'd love to see better pictures of him but my thought on his back are it is what it is, it likely won't ever be a major problem, and I would think he'd be sound for at least light riding if not more. It's ugly, but a roach back doesn't effect them too much. I would geld him if he's not already (don't need that passed on!) and I would also try to find a veterinary chiropractor to look at him at some point (get the regular vets opinion first).
My thought with his hind legs given what I can see is he likely has locking stifles. You can look up videos on youtube see how they compare. This can be a phase even a well built foal can go through and if he has poor conformation that will make it worse. You can do exercises to strengthen the stifles and he may possibly grow out of it, but I'm guessing it will always be a weak point for him, especially if conformational. Of course, this is just a hunch going off his build in the picture.
Did you send the pictures and video to your vet? The video can be uploaded to youtube and then a link pasted here, I don't think you can upload it directly.
I think his weight is ok right now, your next step is mostly just the time and proper care to fix the malnourishment issues and keep him growing well.
Do check out a chiropractor for him.