My iPhone backup stopped halfway through because my Mac ran out of space for it. Now there's 50 GB worth of iPhone data that actually did back up and I can't find it and delete it. How do I access it?

Not sure if you have tried the following -- open iTunes on your MacBook Air, go to iTunes Preferences and click Devices in the bar at the top of the Preferences window, select the backup and then click the "Delete Backup" button.

Also, backups are located at ~/Library/Application Support/MobileSync/Backup/

You can navigate to the Library by opening Finder and then hold down the Option key while using the Go menu in Finder's menu bar