Is it a fair or foul ball if the ball hits a player and lands in foul territory?
Depends on who the player is and where he is when hit by the ball. If player is in fair territory when he is hit it is a fair ball, if he is in foul territory it is foul. If player in on offense (team at bat) he is out if hit in fair territory. If player hit is on defense its playable if he is hit in fair territory and foul if he is hit in foul territory.
Actually, a bit of clarification is needed.
Whether or not a ball is fair or foul has ABSOLUTELY NOTHING to do with the position of the of a fielder, or, for that matter, a base runner being hit. Fair or foul has EVERYTHING to do with the position of THE BALL in relation to the field when it hits said fielder or baserunner.
I've seen situations where managers argue up and down that a fly ball was fair when it was attempted to be caught by a third baseman standing on fair territory on the line was dropped - but that the fielder reached across the line to attempt the catch. The ball however was over foul territory when it struck the player's glove. People sometimes forget that it's ALWAYS the position of THE BALL that is the "defining moment."