I am a novice and would appreciate anyone's advice.

I was just looking in WHM at "Show current CPU usage" and saw several processes running that had "nobody" listed as the owner. They were

proftpd: (accepting connections)
/usr/local/cpanel/bin/startmelange
entropychat
/usr/local/apache/bin/httpd -DSSL

There were several of the last process running.

Should I be concerned about these processes being run by nobody?

Apache will run as nobody unless you have phpsuexec enabled.

Having it run as user nobody will cause problems with some scripts (ie scripts that upload files -- become owned as nobody:nobody and not the user) as well as in determining spam sources.