They are always in the cloud.

If you use the photos app to export the photos then full size ones are downloaded and exported from iCloud even if your computer only had a oreview

What do you mean by moved off. If you mean deleted then deleting it on the iPhone or computer deletes it from both of those and iCloud. Ie iCloud is a syncing service. It keeps all three in sync. You can use an option to limit how much space it takes on your phone and computer in which case it will keep full copies on iCloud and previews in your phone and computer. Or you tell it to also store full copies on your computer.