Rated 5 out of 5 stars
Thank you for your important question.
Instantfox itself doesn't save or transfer any information anywhere. Instantfox uses the same API's when you use for example the Google or Wikipedia Searchbox.
E.g. the Google Suggest API: http://suggestqueries.google.com/complete/search?json&client=firefox&q=%q&hl=de + the Google search-result page.
Google does of course save search analytics information, but if you doesn't like Google, simply delete it and use Bing or DuckduckGo:
If you have any further questions, don't hesitate to ask!