Firefox does not provide web hosting services, it is a web browser, this has nothing to do with Firefox.

I know Firefox is a web browser and not a hosting company, but as I understand it, web browsers allow web developers to register websites on their site so when people search in their browser, the site would be found. By registering I am simply adding my web address to Firefox's database.

mozilla doesn't have its own database but includes or allows users to istall search plugins for google, yahoo, bing and others. so as long as your site is indexed by those common search providers you're all set...

Thank you!