Extensions that do not have a "Remove" button are installed by other software and are not under control of the Firefox extension manager.
Such globally installed extensions are usually found via a registry scan or are installed in a location that Firefox scans for installed extensions.

• https://developer.mozilla.org/en/Adding_Extensions_using_the_Windows_Registry

Extensions installed this way need to be removed via the settings (options/preferences) of the program that has added this extension or you need to uninstall this program via the Control Panel.
In Firefox you an only disable such an extension.

• http://kb.mozillazine.org/Uninstalling_add-ons
• http://kb.mozillazine.org/Uninstalling_toolbars

• http://info.delta-search.com/uninstall/firefox.html

It sounds like you have a third party program that has taken over your search engine, home page, and/or the default new tab page. Fortunately, this can be remedied easily:

install the Search Reset Tool. This will remove the traces of this program from Firefox.

and remove a possible user.js file in your profile folder

• https://support.mozilla.org/en-US/kb/how-to-fix-preferences-wont-save#w_user-js-file-overriding-preferences

For further information, please read Remove a toolbar that has taken over your Firefox search or home page.

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