I want to rent a movie to watch during a flight. How long do I tunes movie rentals last and will it play in airplane mode from my iPad?

You should be able to watch it in your iPad if it's been fully downloaded to the Videos app. In terms of how long you have the rental for, then from the page that you posted from :

You have 30 days from the time of rental to watch your movie, and 24 hours (in the US) or 48 hours (elsewhere) after you've started viewing to finish it. Once the rental period expires, the movie will disappear from your iTunes library.