You are starting your descent with your knees(in the Back Squat Vid). Don't do that. Tink about your hips. Stretch your hammies and back well before you even touch a bar. You are not hitting even near parallel in the BS.
As already mentioned, look up(I find forward is best for me but I suck ast squatting). Chest up, abs tight.
How tall are you? I'm no expert but it looks like you have shitty squatting leverages
-Head up, look forward not at the floor. Keep that chest up.
-Pull your hips back at the start of the motion then sit down into the squat - you seem to be leaning forward slightly because you're not pulling your hips back. That slight forward lean gets worse the lower down you go cause its pushing you into the floor.
-Your arms shouldnt be horizontal, they should be vertical.
I think if you sort the position of your arms out, and not let the weight push you down, you'll sort a lot of problems out.
Also, try a slightly wider stance and see how that feels. Feet pointed out slightly, pushing the knees out and not letting them fall in.
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as for arching the back and balance, try with goblet squats to get used to the motion. your lower extremities might be too tight, so just keep working at it and arch your back through the whole motion.
as for shitty leverages, i've stopped falling back on that one once i realized that a large proportion of nfl athletes are way taller than me and squat way more. i've actually come to love a front squat with a huge range of motion (i'm only 6'1 though) and i rest easy knowing that my legs get in more work per rep than my stubbier weightroom compatriots
1) head still isnt up - just keep your head up and your chest will rise a bit naturally.
2) Too much bending at the knees still. Keep the weight on the heel of your foot you should find it harder to lean forward like that.
3) Post another video when you've sorted those things out
4) Just keep at it and dont let it frustrate you
EDIT: Work on hip mobility and hamstring/hip flexability. I think you could benefit from the stretch that guy does in the 8 min video where he gets into his squat, and uses the rack to open his hips up and get a stretch.