How do I go to a website WITHOUT using Google?
This is an older iMac. I already use Firefox on "my" side, which is most of the time. I hardly ever use "his" side, but I need to use it to register something under his email. Apple no longer updates our Safari as it's too old; therefore I NEED to use another browser to stay safe. I downloaded Firefox tonight for "his" side--and now I can't even go to the website I need WITHOUT going thru Google (whose nosiness I HATE). 1) SO WHAT SHOULD I DO? Second question: How do I get to his "Currently AT&T" Emails through Firefox?
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Oh you can just disable that and switch any other search provider as the default, see Add or remove a search engine in Firefox — if you don't need a search engine at all you can e.g. put Wikipedia there and use the searchbox for quick wiki lookups etc. — or set up anything custom (Qwant, Ecosia, Startpage, eBay… pretty much any site that has search functionality can be used in that place) — the article covers all the scenarios.
(As for whether some provider is needed to log in to a specific account/service and how and where to access your emails is not something that changes between browsers — so use the same addresses and accounts as in any previous browsers. If you rely on older bookmarks, you can bring them over too: Importing Safari data into Firefox)