That's a huge set of questions - you're looking at a textbook worth of answers there.
A couple of places to start would be to check out Science and Practice of Strength Training by Dr. Z, a decent conceptual biomechanics book (you can go quantitative if you want obviously), and a text encompassing general human and exercise physiology.
Once you have that generally down, you do an analysis of the demands of a sport (biomechanical, physiological, psychological, etc), the time frame, the current condition of the athlete, and how to best go about improving what needs to be improved with the time/equipment available.
The NSCA textbook does a pretty good job explaining how to coach/train an athlete as well, but it doesn't go much into the whys of physics/physiology.
I'm sure others will have some resource suggestions as well, these are just a couple off the top of my head.
short responses to your questions below