Q: Photo Importing

The iPhone does not support Bluetooth pairing with a computer. It does support AirDrop (which requires Bluetooth to be on but the devices are not paired). However that will only work with 2012 or later Macs. There is more information at Use AirDrop to send files from your Mac to another nearby Mac or iOS device - Apple Support

You should be able to do it via USB cable -- but note that iTunes is not involved (iTunes can be used to send photos the other direction). See the following for information on importing photos from an iPhone to a computer via USB: Import photos and videos from your iPhone, iPad, or iPod touch to your Mac or Windows PC - Apple Support

Another method is via 3rd party apps such as http://www.photosync-app.com

You could also do it via Photo Stream -- but only for photos taken after you turn on Photo Stream: My Photo Stream FAQ - Apple Support

Additionally, If you are using the Photos app on the MacBook Air and you want all of your photos to be on your iPhone, your Mac, and iCloud you could turn on iCloud Photo Library on both the Mac and the phone. Be sure to review the Optimize Storage option in order to reduce the storage space required on the phone and/or the Mac: iCloud Photo Library FAQ - Apple Support