Hi there,
Spotify on Apple Watch only works as a remote for controlling playback on your iPhone, it does not work as a standalone app. Below is a link to the Spotify website detailing Spotify on the Apple Watch:
https://support.spotify.com/us/listen_everywhere/smart_watches/apple-watch/
To use your watch as a standalone music player without your phone, you will need to use the built in Apple Music app on your watch (note this does not require an Apple Music Subscription). Here, you can listen to songs either from Apple Music or your iTunes library.
As for the mobile plan with your Watch, you can use a mobile plan for your watch only if you have the cellular model. When buying a watch new from the Apple store (https://www.apple.com/shop/buy-watch/apple-watch), Apple shows you the supported mobile carriers on the customization page before you purchase the watch. (It does not seem like Boost Mobile is supported, sorry).
I hope that helps, if something is not clear or you have another question, feel free to ask :)