If the ball hits the back of home plate and then comes and hits you and then goes into fair territory is it fair or foul?

The answer to this lies in the definitions listed in Rule 2 of the MLB rule book. FAIR TERRITORY is that part of the playing field within, and including the first base and third base lines, from home base to the bottom of the playing field fence and perpendicularly upwards. All foul lines are in fair territory. A FOUL BALL is a batted ball that settles on foul territory between home and first base, or between home and third base, or that bounds past first or third base on or over foul territory, or that first falls on foul territory beyond first or third base, or that, while on or over foul territory, touches the person of an umpire or player, or any object foreign to the natural ground. From these you will gather that home plate is entirely within fair territory so a ball hitting home plate is still "fair". However, if the "you" in this example is the batter, catcher or umpire and the part of their bodies that the ball touches in on or over foul territory, the ball becomes foul at that point and remains foul no matter what happens afterward. If, however, in the umpire's judgement, the contact is made on or over fair territory, and the ball remains in fair territory, the ball would be fair. In addition, if the umpire determine that the bass is fair, and the "you" is the batter, then the batter would be out.