Bench press is a full body lift. Your initial setup looks like it takes some thought, and that’s a good thing. You lost it when you pulled it out of the rack and immediately brought it down. Pull it out with big air, hold it steady, and let the weight of that barbell smash you a little bit deeper and tigher into the bench. You want to be TIGHT. You got into everything like you were going to be tight, but got loose the minute you unracked. Benching, when you’re tight, the entire lift hurts.
If you have a decent spotter, he can help you unrack without losing tightness.
When you pull it down, you should literally feel your lats activating to keep you tight and keep that bar steady. Don’t just let the bar come down, dictate how it comes down.
When you begin the press, kick into your heels (without raising your ass from the bench). If your ass is coming up, widen your stance. This may take stretching and flexibility work. You may not be able to get leg drive when you’re up on your toes like you are now. Again, stretching and flexibility.
I’m personally bad with elbows, but make sure they don’t flare out - keep them tucked in. Sitting at your computer, pull an imaginary bar to your chest. Try it once with your shoulders retracted and elbows tucked, and then try it with the flare out - you can see the mechanics and feel how your back works differently.
Your technique may also vary depending on your goals. I’m a powerlifter, and I have a good arch naturally, so I work to get that arch bigger. You’re always going to want to retract your shoulders to some degree as a matter of safety, but you don’t necessarily need to work on an insane high arch.
Also, x999999 on Dave Tate’s cure.