Would an airplane take off with only one passenger?

If it's a one a day flight, probably yes. I have been on a scheduled flight with 2 passengers. If there are hourly flights, they will say the 6 o'clock flight has been delayed a couple of times before putting you on the 7 o'clock flight.

Of course. The aircraft has to follow the schedule or else there will be a missing plane for the next flight. It is the same for buses and trains.

It has happened before as people have posted pictures. It is very rare and usually due to bad weather and the other passengers being re-booked on other flights, but the plane needs to be at that location because there are passengers waiting at that airport. There was a story once of an American Airlines flight that left from New York to London Heathrow with only 5 people on board.

Yes.It doesn't happen that often but it does happen. In fact it happened recently.

https://thepointsguy.com/2017/10/passenger-gets-pr...

http://www.dailymail.co.uk/travel/travel_news/arti...

https://nypost.com/2018/01/04/luckiest-passenger-e...

Private plane, YES.

Commercial plane, it will Never happen

depends on the situation but it happens more than you think. Not necessarily one passenger but anything less than a profitable flight is subject to cancellation. Airplanes fly a certain route so it needs to be somewhere else. A lot of seasonal routes have this issue at the beginning or end of the season. the outbound flight might have only a few people but the return flight might be fully booked so that plane has to be there..

Now, if it's between two cities that the airline has several flights a day, they may cancel an empty flight if it doesn't have to be somewhere else. But again, lot of factors. A small airline with limited aircraft would probably have to run the flight because they have a full a schedule. Routes that are out and back and only serviced once per day will have to go no matter what because there's actually two flights and they won't cancel unless they have no choice. Also, certain routes can only use certain aircraft so might not have any choice.

This is also called repositioning, moving a plane to another city that has a live load

They have. Normally it is because they need the plane at the destination. Sometimes they move a plan to another airport with no passengers. I've flown with just 3 of us.

Yes. Use a search engine to find tons of articles about how a sole passenger facebooked, instagramed or twittered about that happening to them.

If that person was the only one booked on the flight then yes probably

Yes. All airports have an orderly schedule. Even if nobody has purchased a ticket for that plane and there are no passengers the plane will fly to its assigned destination at its assigned time regardless.