To answer your questions:
You don't own the music on spotify, you just have the rights to stream it. The free service allows you to stream from a PC with ads and use the radio app on your phone. The pay service allows you to stream an unlimited amount of music from your PC or Phone, ad-free.
You can allow spotify on your PC to pull in playlists from itunes, but I don't think you can access these playlists on your phone. The playlists you create on spotify should be available on the smartphone app (if you paid for the service).
This post was edited on 10/4 at 2:11 pm