Keep your eyes directly over ball, shoulders parallel and putter face perpendicular to target line and head still
Push shots are caused by a swing that is too shallow and from the inside, many times caused by the body moving in front of the ball during the downswing and causing the club to get stuck behind the body
The four sidehill lies effect the flight of the ball the same way the ball would roll on the ground, so if you are on a sidehill lie above the ball if you were to roll a ball in that direction it would roll off to the right and that is what your ball flight will do