Nah... you asked about the "legality" of it, but also said they would be "made up" call letters...
I can't conceivably think of any reason that would be actionable in any way for using fake call letters. Call letters are assigned to individuals or companies... if no real entity has (or has applied for) a certain designation, then there is no owner/designee to complain or bring an action. It's no different than making up a fake name of a store or business to use in a film.
As for the FCC, I'm not sure they have a position on it (I doubt it, since fake call letters have been used in films numerous times). But even if they didn't like it, they'd have no actionable claim.
As for a made up slogan?... that's a no-brainer. Perfectly legal, not even a gray area.
Fantastic Plastic Entertainment, Inc. fantasticplastic.com