Chris wrote up a nice discussion of the experiment that fills in some of the details. Please take a look at this animation for the Otto Cycle. We don't leave out a step. Yes it does. It represents the waste heat that is expelled to the atmosphere.
Efficiency is defined as work output per fuel burn.
So I need two quantities. The time it takes for the piston to move from the top of the cylinder to the bottom is much shorter than the amount of time it takes to transfer appreciable heat from the walls, so adiabatic is a good assumption. Yes it is. I think I had the signs correct on the board, but maybe I made a mistake. They are correct in the notes.