Squat things to fix

Talked to a friend about some little things with my squat form that could make a big difference when it comes to progress. First of all, the bar moves around a lot on my back, which is no revelation. But he suggested actually changing my grip on the bar, wrapping my thumbs and forcing my wrists to neutral, which might help keep the bar from moving. Furthermore, he told me that every time I squat, the bar is tilted slightly on my back, about 6 or seven degrees, which I should obviously fix (although it will be tricky because I can't really feel it). Furthermore, another reason for the bar moving is the fact that, at the bottom of the rep, I tend to jerk my head back, which makes the bar roll. This also is a problem in and of itself - because I throw my head back in order to arch hard against the bar, is in a broken position, which is never ideal. I need to work on correcting this, keeping my head neutral throughout the movement. Not sure how I got into this bad habit - Josh thinks that it might have to do with my abs/core being the weak link in my squat, and so instead of keeping a stable, neutral spine throughout the movement I throw my head back and arch hard in order to compensate for my possible weaknesses. Won't know until I fix it I guess.

HOPEFULLY, I can fix both the bar movement problem and my broken position without taking any hits to my strength. If I'm lucky, I will be able to work on/fix both of these things without having to take my weights down, and when they are fixed they will help me progress better. I'll just have to focus on them best I can on all my warmup/lighter sets, and make sure I do my 5 x 10 with all beautiful reps (to avoid reinforcing bad habits). That, in conjunction with some hard and heavy ab work, to make sure that my core is not a weak point, and I should slowly but surely be able to right these little issues with technique and make my squat better and stronger.

We will see.