The overall theme for all your lifts is going to be regarding increasing overall tightness. When you are tight throughout your lifts, you can more effectively transfer power from your legs to the rest of your body. As a byproduct of achieving as much tightness as you can, you will not feel 'comfortable' throughout the lifts.
Squat
Starting out at :00 -- Based on how you approached the bar and took your grip, it does not appear as though you are putting enough effort into properly holding the bar. You need to feel as though you are trying to simultaneously crush and pull the bar apart. Squeeze the bar as if you are trying to crush a golf ball -- you should (more or less) see some vascularity in your hands as you squeeze. Really take a second to work the bar deep into your palm. As time goes by, you won't really have to think about it.
:08 - Based on how it kind of looks like you shirt is crumpling together around your upper back make makes it look like you are on the right track with your upper body. However, that all falls apart shortly. You want to get your shoulder blades back and keep them there throughout the set. A good drill to get an idea of how that feels like is to:
In front of a mirror, stand up and hold your arms out as if you were making a T (like on a crucifix). While keeping your arms in the same plane as they started, move both your arms backwards (on the horizontal plane) as if you wanted to make your shoulder blades touch each other. Depending on your flexibility, you'll probably go back around 45 degrees. You do not want to see your shoulders raise up. Take your arms back as far as you can and that will give you an idea of what it feels like to properly retract your scapulae. You want to feel that same tightness in your upper back throughout the lift.
:09 - There's no need to run a marathon between where the bar starts and where you start squatting when you have a weighted bar on your back. One full step is sufficient -- it's not a big deal when you have 230 on your back but it will be a useless energy drain when you have 500. Might as well get in the habit now.
:13 - There's a ton of debate with head position among the big coaches. At the end of the day, it seems like the idea is that it doesn't really matter. Nonetheless, when I started getting my head back (as if i wanted the back of my head to touch the bar) I was able to get tighter. This does not mean that you raise your chin towards the sky, rather, you move your chin closer to the center of your body. It's kind of like you are trying to make a double chin for yourself. Give it a shot -- if it feels makes you feel tighter, than you may want to consider sticking with it. There's a multitude of very strong squatter that use a relaxed (neutral-ish) head positions as well -- go with whatever makes you feel tighter and stronger.
:16-20 - Here's were things kind of go a bit sour and you're not holding onto any tightness. Before you initiate any movement, you need to achieve tightness in your torso. This seems to be pretty common knowledge but for whatever reason, people screw up the execution. For whatever reason, there is a tendencies to 'tighten the core' by sucking in one's gut and trying to contract the muscles. Rather, one can get significantly tighter but taking in a lot of air and then pushing the abdominals out as if you were trying to make your belly look big. This is were a belt comes in -- you can push your stomach out against the belt and the belt will push back. Get a bet. Elitefts.com sells really get ones for about $70. Wherever you choose to get one from, I highly recommend a single-prong belt. I have a double prong from Elitefts and it's a unnecessary pain to get in and out of.
In regard to properly taking in air, a good drill is to try to stand in front of a mirror and take a deep breath. If your shoulders are raising up, you are doing it improperly -- keep working on it until you can 'breathe into your belly'.
:23 - Here's a pretty good indicator of losing tightness. You are starting to lean forward as you are coming up and your chest is getting closer to parallel to the ground. Also, you completely lose the tightness in your shoulders here. At this point, with heavier weights, you'd would have to get rid of the bar over your head and neck in order to avoid toppling over. With properly retracted shoulders, your chest will stay up and facing forward. Overall, your pattern at this point involves squatting down, elevating your lower body, and then asynchronously from your lower body, you're lifting your upper body to return to the proper position.
I can't see the ground but it looks like you have pretty good depth. Also, it's perfectly acceptable to allow yourself to rebound a bit with your hamstrings in the transition between going down and coming up. At higher weights, the rebound will be less pronounced because your descent will be slower.
In regards to breathing: I can't really tell what you are doing but with the squat, hold your breath throughout the rep. Releasing it on the way up is frankly ridiculous -- you are losing all your tightness and you might not be able to lock out at the top. Feel free to take a fresh breath at the top -- maintain your tightness though. With lighter weights, you can hold your breath through perhaps an extra rep or so, but with heavier weights, it's too possible for one's lights to go out before one realizes that they need a fresh breath.
Overall, tightness is the name of the game. Everything needs to be as tight as you possibly can get it --- your hands, upper back, belly -- you needs to feel like you are preparing to get hit by a bus. You'll know you are doing it properly when you feel spent after every set, even the light ones.
That's basically what immediately comes to mind. If you can get some clearer videos with a side view and head-on view, perhaps I'll have some more to say.