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
When training an athelete:
*What type of split approach is most effectively utilized? ( I believe Upper and Lower?)
Depends on the sport and the athlete. Usually full-body with rotated emphasis.
*What kind of techniques are used?
Not quite sure what you’re asking here.
*What model of Periodization should be employed? + How? (Non Linear, indulating, or Conjugate?)
Depends on the time frame and athlete’s condition among other things. Usually undulating or conjugate, linear isn’t used by the best coaches these days much.
*What considerations should come to mind when training an athelete, striving for muscle gain + relative/absolute strength?
Diet and training methods
Yup, all those get cycled - again, for how long/what degree depends on the sport and athlete.
*How would one organize the overall basic premise of the training regimen? (Rep/Sets,the cycling of different qualities, techniques, periodize, progression,exercise organization/selection)
Generally from less to more specific to the sport - build necessary qualities to more effectively improve sport-related skills and prevent injury. A bare-bones example might be barbell squat to split squat to lunge to twisting lunge to Peterson step-ups, or all of those mixed together over weeks as it fits in the overall scheme.
Any help would be appreciated.