For licensing info (including an application for licensing), check out
GreekLicensing.com. It seems to provide licensing for many if not most NPC and NIC/former-NIC groups. It would be a good start at least.
Oh, and for Phi Mu Alpha, I would suggest either a lyre (or harp) or an equilateral triangle. A cat is another possibility, but not just any cat design would do. It would have to conform to some of the historic depictions (which I assume are trademarked) for it to be recognizable as the Mystic Cat.