The lines marking the three foot lane are part of the lane and the batter-runner is required to have both feet within the three foot lane or on the lines marking the lane.
An infield fly is no different than any other fly ball in regard to the runners. The difference is they are never forced to advance because the batter is out whether the ball is caught, or not.
A pitch is a ball delivered to the batter by the pitcher. It doesn’t matter how the pitch reaches the batter. The batter may hit any pitch that is thrown.