2020-11-10
Color identity is set before the game begins and doesn't change during the game, even if your commander is in a hidden zone (like the hand or library) or an effect changes your commander's color.
2020-11-10
If you don't have a commander, you can't activate War Room's last ability at all.
2020-11-10
If your commander has no colors in its color identity, you pay no life to activate War Room's last ability.