If a Brotherhood member or an Avenger takes a Charge/Running Shot, does it count toward your actions that turn? It is considered a move action and the attack does not count as an extra action.

Can a character make multiple psychic blast or mind control attacks, if they have the arrows?

1. 'Free' moves can be used for movement only. Hence Charge/RS cannot be free moves and count towards your actions per turn. This goes for powers like barrier that use a move action also.

2. Short answer: Yes.

You are attacking so its no longer 'just a move'. It costs an action.