Foxtana Pro is the firefox version of Chrometana Pro, an extension that aims to fill the gap left by the original chrometana which was abandoned by its author.

Selecting "Bing + Cortana" will redirect all bing searches and cortana searches redirected to the browser to the search engine of your choice. Telling cortana to "open example.com" will result in Foxtana pro opening example.com.

It's unclear to me what issues you are experiencing with Foxtana Pro. If you are talking about Foxtana Pro not working when firefox isn't already opened (and thus bing is opened instead of another search engine), then that is an issue that I am in the process of fixing.

Edit: Fixed in 1.6 :)