I guess that that would be a very difficult repair. You'd have to completely dissemble the iPod until you only have the case left. You might look at the teardown to look when they got to the case. Which if, if I'm not wrong at the end. I don't have experience with outdenting aluminum things. I think it's possible but it won't look pretty anymore. My advice is searching for a replacement back, or as I do with my MBP, just live with it as long as it doesn't hurt the functioning of the device. I'm sorry for you that you broke your device that fast. There is quite a lot of adhesive that you will have to face until you get to the case. I think that putting all that adhesive back would be quite difficult. The actual outdenting would also be quite the challenge according to me. This image is from the teardown and shows only the backplate for reference.
To answer your questions about the buttons: I've searched a bit on iFixit and I don't see any available parts yet, you'll have to wait until that is added. Yet if you really (and I mean REALLY) want it fixed, the best solution would be to buy a new one, sorry.