I never use snap to grid it's a PITA, you may find that messes things up. If you want to draw vertical or horizontal lines try holding control down as you draw.
In CD you can rotate either manually, click twice, (slowly) and the handles turn to arrows. Click and drag an arrow to rotate. Holding control at the same time constrains movement to a preset number of degrees. You can also change the centre of rotation by dragging the circle with a centre dot to an alternate position. If here is a snap rotate in CD, I haven't found it yet!