AVH-P4200DVD with Bluetooth installed, won't pair with Sharp FX cell phone. Now wondering if it would pair with an 'android' cell phone if I upgraded to a Motorola Bravo cell phone.

The pairing problems are caused by the fact that not all bluetooth device manufacturers follow the standards to the letter. Because of that the pairing is always a hit or miss affair and the only way to know for sure is to check it before buying.
I never used a Sharp FX phone so i can't be absolutely sure in blaming it, but, from my experience, both Pioneer and Motorola follow the standard so there's a very good chance the pairing will work.