you can pair regular bluetooth devices, so the headset should work
the Youtube music app for the watch is just a remote for the phone, not an actual player. So if your phone is in your pocket you can change music from your wrist, but you must have your phone in order to listen to music.
more info
currently Apple Music will let you stream or sync to the watch
Spotify will let you stream (this is a new-ish feature, I think it's available to everyone, but might still be rolling out) previously it was like YouTube, and just a remote for the phone app.
and I believe most of the podcast apps will let you sync podcasts (not sure about streaming) but you'll need to verify before you buy anything.