Is there a way to download all my songs on my iPhone to my Apple Watch?

ALL of your songs might require too much space on your  Watch. To download songs to your  Watch use the Watch app on your iPhone.

Watch app > scroll down to Music > tap Edit in top right corner > Tap Add Music > Select the music you want to add > Tap Done

You iPhone will download the selected music to your watch the following night when both the watch and iPhone are on a charger.

Yes as long as all your music can fit in the Apple Watch storage. See here: Add music to Apple Watch - Apple Support