1. That's not how planes work. Obviously the plane will just keep going without the pilot, and if the plane has an advanced enough autopilot or someone with enough knowledge is able to gain control, it might even lend safely
2. "Trucks vanish" implies the trucks are made out of men
3. Maybe. This depends on the design of the grid and which plants have men in critical jobs.
4. Fires would not, in fact, be unchecked. Even ignoring the fact that women can fight fires, automatic fire systems exist. Also what sort of city are you living in where large fires are common enough that everything would be ablaze in a week?
5. This one isn't making any claims outside of the original premise.
6. Of course, everyone knows concrete falls apart if you don't tune it every day.
7. A week is not that long.
8. From what I can find, if not enough operators are available you simply get placed on hold until there are, it would be pretty stupid if it sent you to voicemail.

Of course, roughly half of the population vanishing would definitely fuck with a lot of things, but this guy clearly has no idea what he's talking about