Do the mouths and noses of cats become impure if they eat from a dog's food? And is it obligatory to wash them seven times, one of which is with earth? And do the hand and clothes become impure by touching these cats afterward, knowing that cats lick themselves and no trace of the food remains?

The dog and its saliva are impure. However, if the food is solid, only the part touched by the dog becomes impure. The mouth of cats is not ruled as impure unless it is confirmed that they directly touched the spot on the food that was affected by the dog. Consequently, what their mouth touches on your body or clothes does not become impure, in accordance with the principle of absence of impurity.

If the impurity of a cat's mouth is confirmed, and then it disappears and it is probable that it drank from water, then many jurists do not rule as impure what it touched. In fact, some jurists hold that its mouth becomes pure by its saliva out of necessity, and this is indicated by the fact that its saliva is not impure despite knowing that it eats impure things.

Based on this, the mouth of the aforementioned cat is not ruled as impure, nor is what it touched of your clothes or anything else.