Pokemon-go – What determines which pokemon you are allowed to place at a gym

Yes, after training at a Pokégym, if your Pokémon takes any damage, they will need to be healed. Note, if your Pokémon loses, he will faint and need to be revived.

source: personal experience

You got kicked out because the Gym was defeated - all the Pokemon on the gym were knocked out, one by one. Some of your Team Mystic teammates then "sniped" the gym - claiming it for Team Mystic by placing Pokemon on to defend it before whoever defeated it could claim the gym for themselves.

The gym going grey was the game showing all the old Pokemon leaving the gym. If you check usernames, you'll probably see that none of the trainers are the same ones you joined when you defended the gym, and all the Pokemon placed there changed too.

Update: The game has put measures in place to prevent sniping. When a gym is defeated, only the victor (one of the players who got the "You defeated the gym" screen) can put pokemon into the gym for about 5 minutes. If they put a pokemon in, the grace period is ended immediately to allow others to join in supporting/defending the gym.