Log4OM

Do I have to set up Administrator privileges and all of the other items under Communicator in order to set up OmniRig control?

No not for Omnirig only if you need to use the communicator to connect to FLDigi, PSTRotator, DM780 etc

administrator privileges are needed only because, by default, windows doesn't allow "inter process" communications using network or TCP without explicit authorization or administrator privileges.
Another way is to "sign" the code with a recognized certificate, but it cost several hundreds of USD/year to buy one and actually it's out of my possibilities for "free" development