All cats are weird, but your cat seems to be bored if she's chasing invisible things.

She a kitten isn't she? The licking she's just curious, it's kinda the same thing that a human baby does, exploring with their mouth.

My cat eats dirt. I guess there's minerals in it that they crave or something. IDK, my cat is a weirdo though, even for a cat.

My old cat would lick my salt lamp. It was made of real salt, even the dog would lick it.

My cat throws himself at you, has a little "jazz hands" dance, walks on his head, loves being outside even in 20 below weather, rain, snow, sunshine, he don't care. He's a very playful and curious cat and can be a great house or a wild outside cat whenever he wants.

So you see, cats are just plain weird, that's one of their selling points though. lol

i had a calico cat not to long ago, but she disappeared...