Are both pieces needed to install... the recessed tp holder and the bracket? Space behind wall is 3.5 inches. Do I need to add wood block to make up difference since both pieces together only 1 3/4"

No, you do not need to add anything else behind the bracket. Tightening the screws in the middle of the fixture will tighten and pull the bracket, or back plate, up snug to the back side of your wall / mounting surface. When the bracket is tightened against the back side of your wall, the fixture will be secured in place.