It can cache music locally – it does some guessing as to what you want by default, but you can also sync specific playlists. Current models have 32gB of storage.
you can but the issue is they limit the media storage to 8gb. :eyeroll. I can see why they'd want to leave some to the OS, but it really defeats half the purpose of 32 on a watch as is if limited to 8GB for media.
As far as I know, only apple music saves it locally but spotify and others can stream if you have LTE. I believe this is just a hold up from spotify and the apis are available though.
As of about a month ago, Spotify can download content to watch too.
LTE but you can download music when on Wifi and keep it stored on the watch.