Squats are improved, good work. However, you initiate the squat by sticking your butt back and breaking at the hips, and THEN you break at the knees. These two events should happen together, meaning at the same time. Hips and knees bend, as you descend, knees find their position about 1/3 of the way down, crease of the hips drop below the patella, then the reverse. Your squat appears to start with almost a backward motion of the knees...this is not good.
Your press has two immediate issues that I see from this video. First, your "lay back" is from the spine (or rather, it appears to be from this video) and not your hips. This is best corrected by the very hard contraction of your abs in concert with your back. Your entire middle section has needs to be rigid as you rotate back about the hip joint. Second, the movement is initiated from the hips, not the the arms. I have found that this is an exceptionally difficult and complex movement to learn.
I may be incorrect about your back/hip part, very hard to see on a video. Do you notice lower back soreness after or during a pressing session? When properly done, I have found that I do not have lower back soreness. However, when bending at the L4/L5/S1 area, I'm sore as crap.
Hope this helps.