1. The 'elbow height' problem is what is known as the front squat rack position, and googling front squat + wrist for example should give you some ideas.
One way to improve this is to load a bar in a rack at chest height, with more weight than you can lift, then step up to the bar and get in the front squat position, ie. bar sitting in the fingers and on top of the delts, then simply try and lift your elbows and stretch it out. You can also do this with a partner gently pushing up on your elbows, but I'd work on it by yourself first. There are other ways too.
2. You are meant to be lifting the bar with your arms (shoulders) - the momentum from the squat should only get the bar above your shoulders and then you press it out. You might be better to learn the front squat and the push press separately to begin with, then merge them into one smooth movement (ie thrusters)
3. The best place to learn thrusters is probably the videos on the Crossfit website.