Where should I put tomcat external libraries

Does tomcat need to be restarted in order to use a new servlet uploaded to the "WEB-INF/classes" directory?

It depends, if your

Does tomcat need to be restarted to read changes to the web.xml in the "WEB-INF" directory?

It depends, if your

If I put a .class file at /WEB-INF/classes/foo/bar.class should I be able to access it immeidately via "http://www.mydomain.com/servlet/foo/bar" or do I need ot wait for tomcat to recognize this new class file?

No, the class will be available to the webapp classloader immediately, if your context is reloadable, see above.

Or do I have to include it in the existing web.xml servlet mapping file?

To access your class (assuming it extends HttpServlet) via HTTP, it will need a mapping in web.xml (assuming you are using straight http servlets)

You can put it anywhere inside <VirtualHost>. So after <Directory>…</Directory> is fine, as is before it, or between ServerName and ServerAlias, etc.

You can probably put it outside the vhost as well, in which case it'll apply to all vhosts (but I'm not completely sure on this).