Can I connect my phone to the Mac air and see it as an external drive?

No. The iPhone will not appear as a drive on Mac.

Photo downloads are not performed through iTunes at all.

You can use the Photos App, or Image Capture to get the photos off of the iPhone. iTunes is not involved.

See here: link-> Transfer images in Image Capture on Mac - Apple Support

and here: link-> Transfer photos and videos from your iPhone, iPad, or iPod touch to your Mac - Apple Support

No. But you can use image capture instead of photos if you wish.