Do tiles need to be cut to fit area between back wall and the edge of the bathtub?
Yes the tile will need to be cut.  You can either use a wet saw or a manual tile cutter.

Before you go cutting the tiles in half for the back wall you will need to make sure you are accounting for the width of the grout lines. Are your tiles really 2"x2"? Do you have bullnose pieces or trim pieces to transition the tile at the edge, or is it OK for your tile to show an exposed edge?