Moving a character doesn't cost any ticks.
If the only thing you do with a character in a turn is move them then their personal clock will match the master clock at the end of the turn. There is a rule that states that if the character's personal clock matches the master clock at the end of the turn you tick them up by 1. But, that's not because moving them cost anything, it's simply because you didn't do anything else that cost anything.
You cannot play a non-instant attack and a non-instant action bar card in the same turn.
The hands of a healer