Yes they do
Mercury is the only metal that is a liquid at room temperature. It is an element, and is dangerous to come in direct contact with
Some batteries, although I don't think they put Mercury in it anymore. Power saving lamps and much much more. You should look it up on google!!
No, the core of mercury is believed to be composed mainly of iron.
Scientists do not yet know if Mercury has the element Mercury in it, they need further studies. AKA they have to get more "inside" of Mercury.