How can I unsnap something when it's snapped?
Any of the following works :
- When focusing on the snapped app, press B to go back until it disappears
- Double press guide, select bottom tile (unsnap)
- Single press guide, select "unsnap" tile
- Single press guide, set focus to app, press "menu", select "Unsnap" (or "Quit", but that would close your app while unsnap will keep it in memory... I suppose)
- Just for fun, you can do all of the above with gestures and/or voice commands : grab the edges of the screen and pull them to the center, say "Xbox display menu" and push "unsnap".

- "Xbox Unsnap"
Also, I've noticed if I try to go into achievements or something like that while a game is running, I just get the achievements for that game. Can't I look at all of them?
Not when snapped. As mentioned above, you must expand it to full screen to have the achievements become independent from the game.
Is there anyway to get the system to shut completely off?
In the system power settings, you can set it to "energy saving" or something like that, which means that it will shut off completely. In that case "Xbox on" won't work, of course.
You can also use the universal "keep pressing the power button for several seconds" which will turn it off completely whatever your power settings (the go-to solution to buggy apps).