Do I have to subscribe to Apple Music to buy one song that I might want?

You do not have to subscribe to Apple Music to purchase a song, it's only for unlimited streaming. To purchase a song on your Mac, you still use the Music app, just make sure Show iTunes Store is checked at Music > Settings > General. You can purchase individual song on the iTunes Store.

You can't buy any songs through Apple Music so, no. You buy music through the iTunes Store. It's a separate app on your phone.