Can't delete /User/Shared

Yes, it's supposed to be there. No, you shouldn't delete it. It isn't related to the file sharing setting in System Preferences. It's for files to be shared by different users of the same computer.

What are the Shared and Public folders?

 

As you start using OSx, be very careful about deleting files/directories if you do not know exactly what the file is for or what other things depend on it.

The same thing applies to file permissions - there are plenty of threads from people who have gone amuck changing file permissions and wind up with a system that will not boot, requiring a reinstall.

 

Yeah. Leave it be. It can even screw with your ability to make purchases in iTunes if you happen to delete it.

As Old-Wiz stated, be VERY careful with deleting stuff. Generally don't touch anything in the system folder or library folder. Those are definite no touch zones, unless you know EXACTLY the file you're looking for.