don't use xp, it is no longer supported, the only way to stop anything from invading your pricavy is to just stop using it. Everything is invading everyone's pricavy at this point in time.

Well one computer uses XP but my other uses Windows 7 so that isn't the answer but thank you for the kind reply.

Have your tried running firefox in always private browsing mode?

Could you explain what you mean by

using up large amounts of computer space ...
Firefox begins farming information of my searches
 ... invasion of my privacy by Firefox. 

Please expand the explanation of the above to say what you have discovered.

Is this problem only on specific sites ? If so and the sites are publicly accessible without logging in what are the sites in question ? Do you seem the same problems with other browsers, such as IE on the Win7 machine ? (If so it may not be a Firefox issue)

As already pointed out XP is no longer supported by Microsoft. It would be better to use a supported OS. Firefox does still support XP more than can be said for Internet Explorer (IIRC they {M.S.) did backport one security fix after saying support had finally ended).

This forum is not for discussion or Advocacy of different OS s but you could consider using Linux if your XP machine is not being upgraded to a Supported Windows OS.

Do I understand correctly that you see the same issue in Windows XP & Windows 7.

farming ?? Do you mean pharming as described here? https://en.wikipedia.org/wiki/Pharming

Or what do you mean by "farming"?