One time I thought I was gonna have a seizure, I layed down and curled up saying fml, and my cat came running from the other room and layed on my chest. No seizure. love you buddy, my familiar.

Greebles! There's a Greebles in the corner and it can't let it escape

What if my cat looks at a wall from 1 inch away ? Is it a really flat ghost ?

Fun fact: the most likely actual reason your cat or dog seems to suddenly go alert and start staring, barking/mewling, and other weird startle behaviors is actually because their hearing is many times more sensitive than yours. So yes, they can detect things you can't, but instead of ghosts it's probably a person or an animal outside. Their hearing also don't "turn off" when they sleep like ours do, they are still constantly processing sound information to almost the same extent as when they're awake.

Its probably a bug. You should submit a report and reboot the cat. Try and see if you can replicate the bug.

Is this what greebles look like?

My cat does this all the time. I guess my apartment is haunted

If the latest string of cat-in-shopping-bag photos is anything to go by:

It's not a bug, it's a bag.