Is it possible for me to set a timer for the Tor Browser window to close automatically if no activity is detected. Or could Tor Browser be set to do this automaticlly when I visit banking websites or other potentially sensitive pages?
You probably can't do this without installing 3rd-party plugins (which you should not do at all, unless you absolutly sure they are not using internet). But there is a button in Tor Browser called New Identity. It's automaticly clears all your cookies and other sensetive data and changes your circuits. You can see it here: