I was on a 739 the other day, temps were around freezing. Normally, after pushback, I hear one of the engines spin up. Then either immediately after or near the runway, I hear the other one spin up. This time, after the first engine spun up, I heard the second one spin up, but then it sounded like it was spinning down. After being delayed an hour, I was getting worried. But a few min later, I heard it spin up again and then we went out to the runway. I assume the engine failed to start the first time if my hearing was right.

Question, how common is it for an engine to fail to start on the first try? If it successfully starts the second time, are there additional checks that are required because it took two tries?

Also, I was at ORD and noticed that most of the field was packed snow/ice covered (maybe 1in) except the runway. Also parts were dug out so you could see some of the lines. I could see tracks sliding around a little when they tried to stop. I know that engine thrust is used to move forward, but I assume that wheel brakes are used to stop. Is this of concern with taxing?