My answer was a little brief. I used to officiate HS ball, so this may be a bit off, but the rules are pretty close.
After any receiving team member makes a valid or invalid fair catch signal, the receiver cannot advance the ball regardless of what happens, unless the ball touches a kicking team member first.
If the receiver makes a catch after a valid fair catch signal, the receiving team is awarded a fair catch and has protection against the kicking team. After a fair catch, the receiving team can attempt a free kick for 3 points.
If the ball hits the ground first after a fair catch signal and is then possessed by the receiving team, there is also no fair catch awarded (no catch was made, after all), and there are is no protection. The ball is dead at the spot.
If the receiver makes a catch after an invalid fair catch signal, he has no protection, cannot advance the ball and will not be awarded a fair catch. The ball is dead at the spot.