Is there a way to deactivate the divider line links/Last Modified Date links? Can I hide the Update pages so that they cannot be viewed without a password?

There is a way to deactivate the links to your Update pages (top divider line in Classic/Classic Frame, Last Modified Date link in Template), and update the website using a different method.

If you would like to do this, go to your Update Index, then click the Site Settings tab.  Click the Customize Web button.  Under "Hide Update pages", you can mark the checkbox to deactivate your top divider line/Last Modified Date links.

If you activate this option, you can update your pages by going to your Update Index (which is always password-protected), then clicking the Update link for the page you'd like to update.

Meanwhile, please note that your site is fully secure, whether or not this option is active.  No one can make updates to your site without access to your password.  The Update pages are visible, but they are designed so that no private information is displayed here.  Still, the option to hide the update sections is available for those who wish to use it.