Apple Ipod downloading

My son has an Apple ipod, I think it has like 5GB that it came with on storage? I paid $20 per year for extra icloud storage. I think he has 15GB. He's used 3.4 GB and I keep trying to download a $5 game but it says he has no storage and that I can manage the storage by going to settings. I can see where there is the 15GB back up but is that not the right thing? I don't know what I'm doing...

Help....

Another question... I just went to icloud... where is all this stuff that is backed up? How do you get to it? My screen looks nothing like it did on my old computer... so confused....