You have not mentioned which side she cut longer than the other. However, there is a certain short hairstyle where one side is longer than the other. That is when you partition your hair from the side, the side that has more hair is left longer from the front and the hair on the rest of the head are shorter. This is quite in and looks great if styled properly.
Yes also with the back tapered..even buzzed..very in
Yes..it's called an asymmetrical haircut/bob..very nice!
Yes it is indeed a new hairstyle and is very popular among girls these days. If you still have doubts then you can check Rihanna's new hairdo, who happens to be a young and popular American RnB singer. Your hair dresser certainly knew what she was doing. If you are still confused you can check out www.salonweb.com for further details.