Rated 5 out of 5 stars

This truly is a superior extension. It brings Chrome's powerful omnibar search to Firefox - but makes it faster and more customizable. Thanks developers! This is a must have for any Firefox user. My only concern is the privacy policy. I'd like more documentation about how our privacy is affected when using this extension.

This review is for a previous version of the add-on (2.7.1). 

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:
http://duckduckgo.com/?q=%q

If you have any further questions, don't hesitate to ask!