Is it possible to remove the "Shared" folder under Users? Under "Sharing" in System Preferences, I do not have anything shared. However, I have a "Shared" folder under "Users". Is there a way to remove this folder?
Yes, it's possible, but that doesn't mean you should do it.

Finder/etc doesn't stop you deleting it, and it's not a 'system' directory (despite being created by the system), but is it causing a problem, enough that you want to delete it? Apps can depend on that directory and deleting it could cause problems, now or in the future. I don't have any examples of such applications, but that's not to say they don't exist or may exist in the future.