I just bought movie in iTunes but I need to be online to watch it. Can I download it to my ipadAir?

Yes. You should be able to download a hard copy onto your iPad Air. Click on the 'Videos' app icon from your iPad Air and you will see all the movies and TV Shows that you have purchased. There should be a small icon that looks like a cloud on the corner of each cover of the movies you bought. Click on it and you can either watch the movie via Wifi (by clicking on the 'play arrow' icon) or click on the 'cloud' icon to download the movie onto your iPad Air.