I'd say, edit them where it's the most convenient / comfortable for you -- Snapseed has more ready to use "looks" and good tools with a lot of tweaking allowed, but doesn't do full res images and is destructive. The Gallery editor is more oriented toward precise photo editing and flexible workflow, allows non-destructive edits and full-size processing, and is integrated with Gallery (duh), but doesn't ship with the Snapseed looks. Both are usable on your device without needing an internet connection, so the choice between them would probably depends on which UI you like the most and which features you prefer.
The other choice, more integrated with Google, is the G+ Photos editor, which actually allows non-destructive edits and saving in the cloud (yay!), but has less tools and effects than Snapseed or the Gallery Editor for now.+Tee YingKiat
no, it works with JPEG files (i.e. what the device Camera uses).+marc lindner
no, that pic was taken by +John Hoford
a few years ago I think, I'd guess with a nikon dslr.