Delete photos from MacBook

The only way to delete photos from your Library, but keeping them in iCloud would be to disable iCloud Photos on your Mac.

Then you can delete photos from in Photos on your Mac and they will stay in iCloud. But you can no longer access the photos in iCloud from your Mac using the Photos.app on your Mac. It would be highly inconvenient. I cannot recommend to do that.

Tt would be better to enable "Optimise Mac Storage" in the Photos Preferences > iCloud. Then you can save some storage, because Photos will remove high resolution originals, the depth map of portrait photos, the video components of Live Photos automatically, when your are low on storage on your MacBook Air.

Not as long as they are all connected to the same iCloud Photos library. iCloud Photos is a full-sync service; all devices connected to the same library contain the same photos.