For the squat, you're definitely not tight enough. You need to be tight from head to toe, as that'll lock you in position and let the bar travel in a vertical line up and down. With the shoulder/wrist pain try any or all of the following: move your grip out; go thumbless' put your pinkie under the bar. High vs low bar is really a personal preference, but I think if you fix your grip you'll be able to squat low bar quite comfortably.
To get tight, start by driving your head hard back into the bar; pull the bar down into your shoulders as if you're trying to bend it; and pull your elbows under the bar. That'll pretty much take care of keeping your chest up. Get a big bellyful of air and squeeze down on it from all directions, squeeze your glutes and go straight down (not too fast, because you'll lose your tightness) pushing your knees out (if you squat wider, it might be better to pull your butt back rather than straight down, but it looks like you're not squatting so wide). Hit depth and reverse direction hard and fast, keep pushing the knees out and lead with your chest.
For the deadlift, there are a few things you should probably work on. First, get tight (again). It's a bit simpler for the deadlift IMO, just fill your belly with air and squeeze down on it before you drop to grip the bar. With the pull itself, your hips shoot up before the bar actually leaves the ground so you're not getting much leg drive off the ground at all. That could be a weakness in the hamstrings themselves along with less than optimal technique. The weakness is an easy fix, just do a bunch of GHRs and some good mornings. Technique isn't a hard fix either. Your back rounding is also probably a mix of weakness/technique, although getting tight will make a huge difference. For the strength side, do lots of rows and chins along with good mornings as well as front squats. Those will also strengthen your whole back and make it easier to stay rigid, which will translate well to your squat too.
In terms of technique for the deadlift I would recommend the following:
- when standing at the bar, make sure it is over your mid-foot
- get tight
- drop to grip the bar and pull it into your shins keeping your shoulders behind the bar
- point the bottom of your ribcage at the floor: this will a) get your back into a good position and b) put your hips where they should be
- push hard and fast off the floor without shooting your hips up too early or letting your shoulders drift forward
- throughout the movement pull the bar into you rather than up and keep your weight behind the bar
- once the bar is moving, then you push your hips through