Hey man, I've got some bad news, you're simply being really hard on yourself. Your squats look really good to me.
Here's what's happening, you likely have 1 glute that isn't firing, and it's making your compensate. Keep on with the single leg hip thrusts, and that should even it out, but read Bret Contreras' advanced glute training article on here.
I never posted this warm up, but do this exactly before you train, should loosen up your hips enough that you don't have one higher than the other, or one foot in front of the other.
I'd also highly advise you to ditch 531 for now, and focus your energies on sheiko. Google sheiko #29, and find a good english version and do that, along wit the warm up and single leg hip thusts. I like sheikko for you right now, as the low reps will help your form, whereas 531 you're always doing higher reps, at least I did, and I tended to breakdown... sure got strong though.
Once again, I'm sorry I couldn't be more help, but I think you're doing great, focus on the above and don't be so hard on yourself, it's supposed to be fun.
and feel free to answer as many questions as you want, and post as many videos as you want, I'll always watch them and do my best to help out.
Thank you very much for the attention! You helped me a lot. I know that the problem is in my left glute now and I am working on it. As for the warmup you showed me - I did this when I was on Blood and Guts(very nice program btw). I can do the unilateral leg raise with a really straight leg and the other one lying on the ground also straight :) I do this for stretching but I also add my hand to help it get further. So far I managed to get my quads touch my chest with straight knees. I will try some variations now.
