I take really quick short breathes every bar or two, just find that spot before the pickup note (last note of the bar).
Very common to alternate between the major and minor 3rd in this type of stuff… regardless if the song is in a major or minor key.
If it’s a major key and you play the minor 3rd it gives a very nasty sound in which case I love to dirty it up a bit with a growl….very effective.
So yes, this tune is in G and there is much alternating between the B and Bb.
I must say, the song is a breeze on the alto, but for the tenor I need to work on those altissimo notes. Will look at your course on that in the near future.