try arching your back more, pulling your traps together and squeezing your lats as if you were going to bend the barbell in half. On the press, just keep your feet planted on the ground and thrust out with your pelvis but do not let it come off the bench.
As a matter of fact, before you even unrack the weight try practicing getting into position to get a feel for what your body should be doing on every lift.
On a max attempt every muscle in your body should feel like it wants to explode. This is only possible with your feet anchored to the ground.
Practice, practice, practice.