Q: Firefox does not update itself via the help menu When I click the 'Check for updates' button in the 'About Firefox' window, it simply gives me the 'Updates available at https://www.mozilla.org/firefox/' message below.

I don't recall fiddling with about:config recently so I have no idea what might have caused such behaviour. I run Firefox 45.0.2 x86_64 under Windows 7 Enterprise x86_64. I have automatic updates turned off.

A: This appears to be an issue with your ability to store the update on your machine. Ensure that you have full permissions (especially Write) for the %LocalAppData%\Mozilla\updates folder (which should translate to something similar to C:\Users\<USERNAME>\AppData\Local\Mozilla\updates).
This might also be an issue to do with the fact that you have automatic updates turned off. During my testing, I was unable to reproduce the message when the settings app.update.auto, app.update.enabled and app.update.service.enabled were all set to true. Try modifying all three of these (available through about:config) to true and seeing if your issue persists.
Explanation
After looking through the Firefox source code, it seems that the Updates available at https://www.mozilla.org/firefox/ text is displayed in aboutDialog-appUpdater.js when gAppUpdater.aus.canApplyUpdates is false. The following text in the documentation of nsIApplicationUpdateService describes the value of canApplyUpdates:

true if the Update Service can download and install updates. Indicates if the current user has access privileges to the install directory. Read only.

This would imply that you don't have the correct access to the Firefox install directory (C:\Program Files (x86)\Mozilla Firefox on my machine), but after some testing it appears that removing write access to %LocalAppData%\Mozilla\updates\ (along with changing the above app.update settings to false) will cause the message to appear. Not having access to the installation directory may also pose a problem, but since it isn't getting to the point of applying the update (and therefore modifying installation files), it appears that this isn't the issue you're currently facing.
