1. Deep squat: I have trouble pushing the weight up from the sitting position of a deep squat. Are there specific things I can do to improve my thrust from that position?
Here is a picture to help :
Ummm, lower the weight, perhaps?
Not trying to be a smartass, really I'm not, but it's the first thing you should ordinarily consider when you can't do a full rep of any exercise with proper form. Specially when you're doing full ROM squats.
Remove a few plates until you reach a weight that you CAN push up out of the hole. Work up from there over time.
The hole is a bitch. It's the sticking point of the squat. You could try doing low box squats.
Im not doing heavy weight that I cant get up. I just notice that it is tough gettin it going, but once I do the rest of the way is cake.
i shall look into these box squats, once i learn what they are.
Here's how you do box squats: http://www.weightliftingdiscussion.com/boxsquat.html
Remember, the key is to stop flexing your legs slightly while on the box. This forces you to go from a dead stop, as opposed to using elastic energy in your legs.