Fair Catch or Not
 

Here's a scenario:

R1 calls for a fair catch on a scrimmage kick but does not catch the ball in flight. The ball hits the ground and he begins to run. Do you kill the play or let it go? Is there a foul on the play?

If he gives a valid signal (or invalid for that matter) then the play will be over as soon as he possesses the ball. It's not a fair catch since it hit the ground so they can't free kick, etc, but the play is dead when he possesses it. You could flag him for delay of game if you thought he was doing that but I think when you blow the whistle, he'll stop.

WHat if the runner gets hit/tackled after he possesses the ball?

Unless the hit can be classified as a personal foul, you've got nothing.

Once he gives the fair catch signal, for all practical purposes he takes himself out of the play for everything except catching the ball. Even more than that, he takes the team's ability to advance the ball out of play to so even if another teammate picks the ball up, it cannot be advanced.

And make sure you give the defense the benefit of the doubt if the R player looks like he's trying to run. The important thing is to get on the whistle as soon as R gains possession to stop any of the nonsense.

Once there is a fair catch signal given (valid or invalid) there will be NO return. Blow it dead as soon as the ball is possessed or becomes dead.

You mean the ball hits the ground and he picks it up and begins to run with it? Or, as you stated he does not touch the ball or possess it, he just gives a FC signal, lets the ball go its merry way, and he takes off running to who knows where?

A word of caution...don't be too quick to blow the whistle. I did this once on a short free kick and the ball went through the hands of the receiver and was covered by K. One of my two IWs. Make sure R makes the catch but blow it as quickly as possible after that!

Agreed!