Front squat ?s: Yes on the hips, though it's hard to visualize/conceptualize, and you won't lose tightness if you don't want to, just dont over-analyze it; If anything on the front squats, just try to drive your elbows up hard; On every squat, drive those knees out when going up and down. For the majority of lifts, everything is equal going up and down in a rep, but it will also help you keep tight in the hips and maybe help you sit back further.
Also, like everyone else said. You do shoot forward in the squat, especially at the heavier weights.
One technique issue you need to hit is how far you sit back. for that make sure you keep working box squats so you can really sit back far. Your knees look like they shoot way too far forward because of this.
Lastly, Your hips raise faster than your shoulders/chest on the last set pretty noticeably. I think your form in regards to that looks okay, but you need to make sure of a couple things: trap air in your stomach and chest to keep the tension, though i think you're good there? Keep the bar driving down into your back like doing a lat pulldown to keep that tension in your lats to stabilize you.
If all those things are good already then its not form as much as strength needs. I would hammer HEAVY ab work, i prefer standing to transfer it to squats, maybe thats just me (side bends, pulldown abs, sandbag carries or heavy db carries held at chest, kneeling/lunging/standing pallof presses, zercher squats for low/upper back too) and work your back hard and heavy. Make sure your low back is strong so you don't just let your hips do all the work coming out of the whole.