>I'm probably being a bit stupid, but would it be possible to identify the user from cookies, I'm not too sure what cookies actually do but someone told me that if Yahoo record them they can tell what computer has been trying to log into your account.

Not really. A cookie is a piece of data stored on a computer that is later retrievable by the website that set it. It generally only contains a unique ID for the service to lookup and compare to its databases for whatever reasons it wants that data. Sometimes for autologins, or your email address or whatever.

Since they are a third party and free you aren't going to get the same security log access you would get with hosting it privately. But a good password is generally all you need. They have tight security otherwise.