Question 1. : Lunging, as you said, allows the handler to work both sides of the horses brain, gain balance, work on smoothness across all of the horses gaits, and sending communication signals to the horse through body language. Lunging has many other reasons for why it is good. Things such as if someone has a very energetic horse it allows that person to have a way to calm the horse down and get rid of the unwanted energy without completely gasing their horse before a competition. Another reason lunging is good for the horse is that by getting them to think and move their feet the horse is also gaining respect for the trainer. Question 2. : for the horse to make a smaller circle lowering their head licking their lips (thinking) one ear locked onto the trainer