Transferring playlists from one streaming provider to another is difficult, because the catalogues are not identical and songs/albums may be labelled differently.
I don’t think you can do this on an iPhone directly. Spotify on desktop has an import function that you can use. I’ve also had success with https://soundiiz.com.
Yes. A few days ago, in fact. It updates it automatically and it won’t directly tell you when it needs to be restarted. You can check it in the ‘About’ window. Should be 1.0.42.151.XXX
The most reliable and recommended software to move apple music playlists to spotify is MusConv software. I used this software many times to move music. This software is also helpful in export spotify playlist to cs.