There is plenty of anecdotal evidence to suggest cats communicate and sense things in ways that humans don't understand.
I recently read a blog post somewhere (if I find it I'll post it) about a cat that hated the kitchen cupboards being closed. When the cat was asleep in the garage it woke up as soon as the cupboards were closed, and went into the kitchen to paw at them.
Also, widely reported last summer was the story of
Oscar the cat, who seemed to know when nursing home residents were about to die.
As far as understanding human speech and words goes, why not? Dogs certainly do, and cats brains are more similar to ours than they are to dogs. Although I would hate to think they could follow a converstation. It would be the most frustrating experience to not be able to join in!
Regarding the cat number picker test - definitely worth a try. Just make sure to have a good chat first about what you would buy her should you win.