While I have not seen any statistical evidence to confirm it, my understanding is that Enthusiasm affects how well your players play (whether it improves/reduces their individual effectiveness or team ratings I'm not sure of). That being said, TIE will reduce their effectiveness for that single game, while increasing your Enthusiasm rating immediately following it, so as the first responder noted, TIE with Enthusiasm of 7 will play better than with Enthusiasm of 6. Normal plays at their normal effectiveness for that single game while providing no bonus to the rating immediately following the game. CT plays more effective for that single game while penalizing your rating immediately following it.
I am not sure of the actual speed with which Enthusiasm drops daily, but your rating gravitates back to 5, with the speed increased the further you are away from 5, e.g. if you have Enthusiasm of 10, it will drop faster than if you have Enthusiasm of 6.
Stamina does not reset, but it can drop. It can be trained as a skill through Team training, though, meaning you can train the entire team at full training without worrying about minutes played. For that reason, it's probably best to train it during a 2 game week. It's one of the quickest if not THE quickest skill to train, so you should get pops in 1-2 weeks.