You can’t access or delete a users history. This is private data stored deep within the browser. Only a user themselves can delete their own browser history / cookies etc. from the menu bar or settings / preferences.
Closing the current tab / window is easy to do with a stack like ActionHost. You will want to create a simple link or button in your page like this:
<a href="#">Close Window</a>
In the ActionHost stack, set the Trigger Value to the same label as your link (e.g. Close Window), set Action Type to Execute Custom jQuery. In the jQuery Code box, enter:
Now you will have yourself an instant button that should close the current tab or window on any modern browser. A screenshot of the ActionHost settings are shown.