What is in the unwanted tab? Or is it a window?

It is a blank page (not a window), as I set up new pages to be. When I manually open a new tab, it brings up the Firefox homepage. My preference would be for new tabs (that I open) to bring up the same page as I've set as my default homepage (i.e., Google).

https://addons.mozilla.org/en-US/firefox/addon/new-tab-override/ New Tab Override by Sören Hentzschel

New Tab Override allows you to set the page that shows whenever you open a new tab.

OKay---thanks. That sets my preferred default settings for new tabs. I still have the first problem: Whenever I open my browser OR click on the "home"/house icon on the navigation bar, it always goes there AND opens a second tab, whether I want one or not. (Just makes an extra tab I have to close every time I log off.)

https://support.mozilla.org/en-US/kb/how-to-set-the-home-page

Type about:config<enter> in the address bar. If a warning screen comes up, press the I Accept the Risk button. At the top of the screen is a search bar. Type browser.startup.homepage

What is the value? Right-click and select Reset to restore its default value; about:home

That worked--for stopping the duplicate tab openings. Don't know why it should be so complicated (having to ask for expert help and technical scripts to accomplish this.... I've happily used Firefox for a decade, now, and didn't have this problem until I had to reinstall it on a new computer.

Also: The "New Tab Override" Add-On was helpful (and solved) making new tabs set to my own SELECTED home page [instead of the Firefox Default homepage, which it's always done before.

Glad to help. Safe Surfing.