What would happen if I told my new housekeeper that I have cameras in my house watching her so she doesn't steal?
I think it's a little creepy. Why do you think this new housekeeper will steal your stuff?
I thought I could make sure she won't steal anything, since she thinks I can fire her if she steals something.
It's kind of disrespectful to bring up the cameras. You shouldn't make the assumption that the person will steal, because it makes you look cruel. If you are that worried about theft, you shouldn't even get a house cleaner.
It's fine. I'm doing this to make my house cleaner, not to make her feel comfortable in my home.
If you do this, your housekeeper will bolt at the first chance she gets and you'll have to find another one. You'll make your life easier if you just trust her.