I was on a website. When I signed up, I was not told that the owner could read our private messages. She read mine and kicked me off because "I said bad things about her". Could I sue her?

Not a chance! A Web site is a privately owned entity. If you walked into a person's home and started bad mouthing them they have every right to throw you out. This is the same.

You should NEVER assume that a WEB site owner cannot read any messages posted on the site. The admins can always do that. In most cases they don't, but the capability exists. It's their playground and they can play with whoever they want.

Agreeing with the above, it's the owners website and if your using PM's for things they disaprove of you can be banned. I suppose if you paid for the service you could ask for that back.