My dog licked a tiny bit of sausage grease from the pan — should I rush to the emergency vet?

No, a single lick of grease is not an emergency. The main risks in sausage come from high salt, fat, and potential onion or garlic powder, but a tiny amount is unlikely to cause poisoning. Watch your dog over the next 12-24 hours for signs of an upset stomach, like vomiting, diarrhea, or excessive thirst from the salt. If you notice any of these, or if you know the sausage contained a lot of onion or garlic, call your vet for advice on how to proceed.