Many golfers have long backswings where their arms keep going, keep in mind that your arms should stop swinging when your body stops turning, shortening your backswing will increase the radius of your swing and actually give you more distance
When you begin your puttting practice start by dragging two footers into the cup without a backswing, this is going to make you concentrate on keeping the face square and give you the confidence of watching balls go into the hole
Practice this hitting under a rope drill to help keep your hands forward at impact and avoid an early release of the clubhead