Sounds horrible......"Firefox can deliver on-screen notifications even when that site isn’t loaded"

[friendly_iconoclast]

1. Where's the problem? If you don't opt-in beforehand, you won't get push messages or updates

*Only* sites that you allow beforehand to send notifications can do this
From the page you linked to:

How do I revoke Web Push permissions?

Web Push is always opt-in in Firefox. A site cannot send you push messages without your permission. To stop a specific site from sending you push messages:

Go to the Firefox menu New Fx Menu and select Options.
Select the Content panel and click the Choose… button under Notifications.
Select the site.
Click Remove Site.

To stop all sites from sending you push messages, follow the above steps except, instead of selecting a specific site, click Remove All Sites. Websites will not be able to send you messages and will need to ask your permission to send them in the future.