When does this happen? At startup, or clicking a link, or using a bookmark, or all three?

Could you test in Firefox's Safe Mode? That's a standard diagnostic tool to deactivate extensions and some advanced features of Firefox. More info: Diagnose Firefox issues using Troubleshoot Mode.

If Firefox is not running: Hold down the option key when starting Firefox.

If Firefox is running: You can restart Firefox in Safe Mode using either:

• "3-bar" menu button > "?" button > Restart with Add-ons Disabled
• (menu bar) Help > Restart with Add-ons Disabled

and OK the restart.

Both scenarios: A small dialog should appear. Click "Start in Safe Mode" (not Refresh).

Do things work more normally?

By the way, if Safe Mode works well, a bad add-on is a likely culprit. Let's try to get rid of that.

Open Firefox's Add-ons page using either:

• Command+Shift+a
• "3-bar" menu button (or Tools menu) > Add-ons

In the left column, click Extensions. Then, if in doubt, disable (or Remove, if possible) unrecognized and unwanted extensions. Note: In Safe Mode, extensions are disabled automatically so the Disable button might not be available.

Often a link will appear above at least one disabled extension to restart Firefox. You can complete your work on the tab and click one of the links as the last step.

Any improvement?

Thank you Jscher2000

It happened at start up. When I was posting the question you kindly answer, I saw a "Refresh Firefox" which it seems to have disabled the Add-ons.

Now the mysterious page is not dowloading, but I have constant "Stop script" warnings, but then that is different issue, right?

Those script messages probably are a different issue. I'm not familiar with the likely causes of that on Mac, however; I'm a Windows guy.

Still thanks again for you help.