How does a dog sweat through its mouth?

Yes, when they so called "pant', or breathe with their mouths open and their tongues out. This is their method of cooling. We sweat to cool, they "pant" to cool.

Dogs sweat through their pads and their mouths. This is because a dog does not have sweat glands anywhere else. That is why when a dog is hot it will sweat a lot and stand in water, because that will...

they dont really sweat they drool

They don't sweat.

Yes, they do this when they are panting.