Team B receives serve and over passes the volleyball towards team A. The ball is high and crosses the plane of the net in the front zone of team A's court. The middle blocker of team A approaches in an attacking motion, swings his arm contacting the ball above the height of the net and hits the ball into the net. Then the middle blocker from team A plays the ball again and his team completes 2 more contacts to return the ball to team B. Is this a legal play by team A?
By defintion, a attack hit is not a block (Rule 13.1.1):
All actions which direct the ball towards the opponent, with the exception of service and block, are considered as attack hits.
(my emphasis). However, that's not really the question you're asking here, which is "was the action of the middle blocker on team A a block or an attack hit?". For this, refer to Rule 14.1.1:
Blocking is the action of players close to the net to intercept the ball coming from the opponent by reaching higher than the top of the net, regardless of the height of the ball contact.
From the sound of it, the middle blocker's action was not an attempt to intercept the ball, but instead a separate attempt to spike the ball, so it should not be counted as a block and team A should be whistled for a double hit. This is always a judgement call on the part of the referee, but most cases are fairly obvious.