Welcome to the Spotify Community and thanks for posting your questions here.
If you download an album on your iPhone, the same won't automatically happen on your other two devices, so you'd need to download the album on each of them. It'd be great to check this support site article if you'd like to know more about downloading music on Spotify.
Regarding your last question, with the latest Your Library updates the songs that you 'like' (by clicking the 'heart' symbol next to their title) are now stored in a playlist called Liked Songs. They'll be downloadable just like the songs featured in any other of your playlists.
Hope you'll find this info useful. Let us know if there's anything else we can help with!
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