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.