When defending only troops in the Clan Castle that can attack air targets will come out when only air units enter the range of the Clan Castle. Will the healer come out as well or will she stay in the Clan Castle even if heroes and other Clan Castles are taking damage but no ground troops are deployed by the attacker?
Yes, the healer will come out as well as she will heal your King, Queen, and other ground troops from your cc.
In War, the CC healer will not deploy on dragons. CC Air & ground Wizards will deploy on dragons, but the healer will not deploy to heal them. The CC healer will only deploy when an attacking ground troop comes into CC range. (Seems backwards to me)