The player becomes un ticked if his energy levels are below a certain % this is to prevent you from making mistakes but you can manually select all so its no biggy. The recovery of a player is based of what the original rate is when you buy him + whatever the bonus is you get from your infirmary.
The lower your energy levels while training the less training points you guy will receive, not to sure of the formula tho
Quick tip before purchasing a player go into his general tab and look at his recovery rates i dont look at anything below 2.65 recovery and 150% training but that comes at a price