https://support.mozilla.org/en-US/kb/how-to-fix-preferences-wont-save

Note: Some software, like Advanced SystemCare with Surfing Protection, can protect files in the Firefox profile folder against changes. If you have such software then check the settings or uninstall this software.

Macs: Make sure you install Firefox properly and that you do not run Firefox from within the DMG (Disk Images) file. https://support.mozilla.org/en-US/kb/how-download-and-install-firefox-mac

Sounds like you have malware that is overriding your Firefox settings. (Yahoo! is not a default search engine in Firefox anywhere in the world.)

This may be caused either by an add-on or by external malware. You didn't share your extensions list while posting your question, so here's how to check for problem extensions on your Firefox:

Open the Add-ons page. Either:

• Command+Shift+a (Windows: Ctrl+Shift+a)
• "3-bar" menu button (or Tools menu) > Add-ons
• type or paste about:addons in the address bar and press Enter/Return

In the left column of the Add-ons page, click Extensions. On the right side, find the "Manage Your Extensions" heading.

If there is at least one extension before the next heading -- "Recommended Extensions" -- please continue:

Then cast a critical eye over the list below that heading. Any extensions Firefox installs for built-in features are hidden from this page, so everything listed here is your choice (and your responsibility) to manage. Anything that mentions search, or privacy, or looks suspicious, or that you just do not remember installing or why? If in doubt, disable (or remove). For your privacy and security, don't let mystery programs linger here.

Any improvement?

If your Add-ons page is blank or is blocked, you can restart Firefox in its Safe Mode to do the above review:

In its Safe Mode, Firefox temporarily deactivates extensions, hardware acceleration, and some other advanced features to bypass issues that can cause problems with pages.

If Firefox is running:

You can restart Firefox in Safe/Troubleshoot Mode using either:

• "3-bar" menu button > Help > Troubleshoot Mode... (before Fx88: Restart with Add-ons Disabled)
• (menu bar) Help menu > Troubleshoot Mode... (before Fx88: Restart with Add-ons Disabled)

and OK the restart. A small dialog should appear. Click the Open button (before Fx88: "Start in Safe Mode" button).

If Firefox is not running:

Hold down the option/alt key when starting Firefox. (On Windows, hold down the Shift key instead of the option/alt key.) A small dialog should appear. Click the Open button (before Fx88: "Start in Safe Mode" button).

Note: Don't use the Refresh without first reviewing this article to understand what will be deleted: Refresh Firefox - reset add-ons and settings.

Can you regain control of your search engine setting?

You can try to rename/remove search.json.mozlz4 in the Firefox profile folder with Firefox closed to rebuild the search engines registry.

You can use the button on the "Help -> More Troubleshooting Information" (about:support) page to go to the current Firefox profile folder or use the about:profiles page.

• Help -> More Troubleshooting Information -> Profile Folder/Directory:
  Windows: Open Folder; Linux: Open Directory; Mac: Show in Finder
• https://support.mozilla.org/en-US/kb/profiles-where-firefox-stores-user-data

Firefox will rebuild search.json.mozlz4 from the built-in search engines.