Rules could be different in the US but in the UK he should have turned the power off before checking the auto dialler, this confirms the back up batteries are functioning
Most of these inspections are to ensure that fire service is working properly so that the elevator recalls to the main floor and locks out should there be an emergency in the building.
The open close buttons are plugged in parallel with the main ones. The call cancel wouldn't have any effect as once you press it, it stops at the next floor. This elevator has only two floors.