hi, this certainly sounds like an issue with adware on your system, so please perform all these steps:

1. reset firefox (this will keep your bookmarks and passwords)
2. afterwards go to the firefox menu ≡ > addons > extensions and in case there are still extensions listed there, disable them.
3. finally run a full scan of your system with different security tools like the free version of malwarebytes and adwcleaner to make sure that adware isn't present in other places of your system as well.

Troubleshoot Firefox issues caused by malware

Nigworthy said

Every time I open Firefox I get asked,"Make Firefox your default browser?" which it already is; but it has to be ticked off before I can enter a search. Then whatever I search for, I get diverted to another - commercial - site. These have no relevance to my search, and have to be downloaded before I can turn back a page to where the answers to my search will have been listed. Sometimes they are gambling or betting sites. I don't know if they park cookies on my computer. Is this a virus? My free AVG has scanned my system (it took more than 2 hours) without getting rid of it. Is it a new compromise that comes with Firefox now? Or how can I continue to use Firefox and get rid of it?

Thanks. Main problem sorted; but the bit about making Firefox my default browser carries on.

There is software like Advanced SystemCare with its Surfing Protection feature that can protect files in the Firefox profile folder against changes. If you have such software then check the settings or uninstall this software.

If you do not keep changes after a restart or otherwise have problems with preferences, see:

• http://kb.mozillazine.org/Preferences_not_saved