Type about:addons<enter> in the address bar to open your Add-ons Manager. Hot key; (<Control> [Mac=<Command>] <Shift> A)

In the Add-ons Manager, on the left, select Extensions. Remove “ Google “ Anything.

Also remove SafeSearch, SearchAssist Incognito, FileConverter Addon, SearchLock, DiscreteSearch, WebSearch, Findwide Search Engine

Now do the same in the computer’s Programs Folder.

Windows: Start > Control Panel > Uninstall Programs. Mac: Open the Applications folder. Linux: Check your user manual.

No Google extensions.

It sounds like the site your using isn't the problem but the settings sounds like it is messed up in firefox. Did you look there at your "Options" to see what is set at.

Hi kulajon, instead of removing other search engine plugins, try just "un-checking" them so they don't appear on the one-click search engines list. Any difference?

Your search engine preferences are saved in a file named search.json.mozlz4 in your currently active profile folder (Profiles - Where Firefox stores your bookmarks, passwords and other user data).

Are those the only settings you lose between Firefox sessions?