Does a Facebook tab open, or can you link the request to any particular open page?

If you get an unwanted Facebook page opening at startup, perhaps it was added to your home page(s). You can clean up that list on the Settings page, Home panel. More info in this article: How to set the home page.

Was that the problem?

No, that doesn’t solve the problem. A Facebook page opens and there’s no home button.

When I go to settings in mozilla it says “ your browser is being managed by your organization “ I don’t have an organization

Yup , I did that. And I uninstalled firefox and re-installed it several times. Can’t get rid of facebook

So when the Facebook page opens:

• If you press Ctrl+N to open a new window, is it a normal window?
• If you press Ctrl+W (close tab) on the Facebook popup, does it close?

When I go to settings in mozilla it says “ your browser is being managed by your organization “ I don’t have an organization

This usually indicates that some software has dropped a settings file that overrides normal Firefox settings. As the first step in investigating that, you can type or paste about:policies in the address bar and press Enter to load that page. On the "Active" panel, it usually says: "The Enterprise Policies service is inactive." Does yours list any policies?