Do websites have to tell you if they collect ientifying information from your computer?

No, but there are various guidelines for certain kinds of businesses to have privacy statements where they tell you what information they will take from you, then government agencies check up on them to find out if they are being truthful, depending on how many people complain.

So for example, if Yahoo has a privacy policy, and you join in agreement with it, then Yahoo changes the policy and you don't notice it changed, your tough luck.

Also, lots of businesses don't know what they are doing, or claim to not know what they are doing. In a lot of the breaches, where our credit card info was handed over to the crooks, the companies claim they did not know what the software they bought and installed was doing.

Nope, you might as well expect it. Even if you make your restriction settings very private (cookies, etc.), I'd still be careful. If you have no idea what I'm talking about above, find a computer geek friend who will gladly explain it to you and how to "help" prevent it.