Those teeth don't look broken to me, just worn down. You see it a fair amount in the typical tennis ball obsessed breeds (BCs, Mals, Labs, etc.) - they aren't at as big a risk of infection as broken teeth afaik. I honestly have no idea why the licking would be related to teeth - when my Maggie had a broken tooth she showed no symptoms at all until it got infected, then she just went off her food because it hurt to eat.
I've seen some dogs lick like that when they are nauseous, though again, not for that long. If it happens at a time where she's between meals it might be worth giving her a snack to see if that helps.
Erin, Ziva, Kestrel, Aerten, and Snipe
Always in our hearts: The Amazing Maggie Mae