And the Favourites will also be synced.
The only thing that will not sync with iCloud Photos to an iPhone or iPad are smart albums from a Mac, because smart albums are not yet supported on the mobile devices. iCloud Photos will store the smart albums, also keywords and titles, and sync them to other Macs, but we cannot see them on the mobile devices.
projects will not be synced at all with iCloud Photos.
The albums and folders from your iPhone should be syncing to your iCloud Photos Library, but it may take a while, until they will appear. Photos will first have to sync and upload all photos and videos, before the albums can be created in iCloud. Don't get nervous, when you are seeing at first only empty albums.