Actually, this should be "The cat licked its fur". "It's" is a shortened version of "it is", so would not work correctly in this sentence. "Its" is usually used when something belongs to something else, like the fur belongs to the cat.
no it is not but its not a bad thing either. i have a cat that has licked her belly enough that her hair is gone almost completely but its not irrated at all she just does it normally (like cleaning the rest of its body)
i don't see why it would be- they don't have poison in their saliva. but, only way their saliva could get into your eye is if it licked your eye, which might hurt because cat tongues are rough. that's the only bad thing i can think of... weird question! lol