I already know that I can uninstall Unity if I'm using Gnome-Shell exclusively, but I'm also wondering if it's safe to uninstall Compiz when I'm only using Gnome-Shell, since as far as I know, Gnome-Shell doesn't use Compiz.
Removing compiz also removes the packages
Thus you will lose the ability to log into the unity or unity-2d desktops.
On my quick test, removing compiz did not stop me logging out and logging back into gnome-shell. You are correct - gnome-shell does not use compiz as its compositing manager, it uses mutter.
It depends on how much you want to remove and change.
Yes, you can remove compiz, it will take a little work to remove unity and potentially unnecessary packages.
See the linked question on how to remove Unity.
Use the following to remove all compiz related packages:
If you do not want to do all this, you can re-install and try the gnome 3 remix
See the UGR (Ubuntu Gnome Remix)
UGR Home page (check the LP and wiki page if you think this link is spam) http://ugr.teampr0xy.net/