Starting to run out of space on the Macbook Air. Since I can download any purchased app to my iPhone anytime I want, i don't need them or want them on my Macbook Air. I already have them not syncing onto the iphone. Can I delete them from the Macbook Air?
Yes - delete any iOS apps from iTunes and as long as you are not syncing apps to that computer, they won't transfer back.
Your data will still be backed up, but not the apps themselves.
You can delete them as long as you're not syncing to the iPhone. I would recommend taking a full backup before. Also make sure you disable automatic downloads of new purchases.
Deleting an app might prevent you from installing it again on your iPhone if it has been deleted there as well and Apple removed it from App Store.