Apple Music has a cloud locker feature, which is the main reason I use it over Spotify. The process isn't as nice as the drag-and-drop into your browser like how Google Play Music did it (RIP), but you can add songs through the Music App on Mac (I assume you can also do it through iTunes on Windows?), set all your metadata, etc. and then you can stream it from any device (except the web player, which is among many other problems with the web player. I wouldn't recommend it)
Sure you can. Add those mp3s to the iPhone paired with the Apple Watch. Go to the Watch app and tap on Music. You can choose music to be transferred to the Watch.