I watched a documentry on the Boudica rebellion and in the deciding battle this was exactly what the Romans done and it was one of the the main reasons for their victory.

They probably did use this during this particular battle since its difficult to see how they would have won otherwise.

There must have been some rotation scheme, for reasons of fatigue. However, I doubt it worked this way. Basically, the moment the centurion whistled would be the sign for the enemy to charge, because the legionaries would be packed very close together and therefore unable to attack or defend themselves. More likely, the soldiers would make use of lulls in the fighting to rotate.
I doubt the rotation would leave the soldiers vulnerable. The move would be very quick for experienced soldiers. Hear the whistle (or horn), push the enemy with your massive shield and slip back between your line. Wouldn't take more than a second for the guy behind the frontman to be ready to fight the enemy and the guy moving to the back doesnt exactly turn around and run, he has his shield up until the guy behind is level with him. If the men are extremely tight together then the chance of breaking them is even less likely, it would just be a bit more of a squeeze for the guy at the front to get to the back.

I dont know whether they would have used a horn or a whistle or even just shouted, I would imagine though it was the centurions choice. He would know the men he was with and tell them listen for the whistle or the shout or the horn. I dont think it would be 100% standardized for every battle, could be wrong.