Not sure how to help your hip pain and your squat seems pretty good.
On your press your wrist are cocked back to much, your wrist should only be extended about 15 degrees, this is causing a small moment arm between the bar and your forearms. As well on your press your toes and heels come off the ground due to loss of balance on different reps, you might benefit from a wider stance. Although I can't tell for sure with this angle. You could just use more practice to get your bar path down.