Actually, yes to both. Alligators, crocodiles, gharials, all crocodilians often let birds clean their teeth. Food can get stuck, and this irritates them. This is why crocodilians are often seen on the river banks (or lake) with their mouths open. :]
Crocodiles are cold-blooded, meaning that if they need to cool down they go into the water. If cold, they move onto land in direct sunlight. Dogs are warm-blooded and can't sweat to cool down, so they pant.