As far as I understand, it doesn't keep copies of the different edits. The original file is saved, and the edits are serialized and stored in some form. Only one more copy is generated for the final version for preview and such. When editing again, you can add to or subtract from previous edits, and again a maximum of two files will be present. (But there would be no thumbnail, preview etc. for the original. So it isn't exactly double the storage usage.)

This is my vague recollection from what I've read in the discussions, so take it with a grain of salt. But this is close to what's happening when you're editing.

Did this getting my wife's photos from her iPhone on our server a couple years ago, it works perfectly fine as long as you have storage on the phone still. If a lot of the photos are only in your iCloud backup, it'll have to download them locally do transfer to Immich. We kept running into an issue where it was stuck in a stupid loop of filling up the phone, then trying to offload to iCloud, then trying to redownload them to transfer to Immich. Only a problem if you have more photos/videos than your phone can store and if you're doing it directly from the phone. If everything is already backed up on iCloud you can use something like icloudpd (GitHub link) to do the transfer instead. I have not tested this method

Never used Apple Photos so not sure about the migration. But I can confirm that live photos work just fine.