In Firefox,when you write a question in Google search, immediately you are redirected on a other searcher:QIP search! I can't find if it's a module in the preferences of Firefox
You most likely don't need to do much to "purge" your Firefox. WHen you install it and use it, it creates a hidden directory in your home folder, .mozilla. Just rename that directory to something like .mozilla_old. That way, if this doesn't resolve anything you can get your favorites and stuff back by renaming it back to the original. If it does fix it, delete the old one.
BTW, if all you do is uninstall Firefox and then reinstall Firefox, you will likely have the same issues as these are often profile related. The only way to remove the profile is like I explained above.
Not related, but if you've read some of my other posts, you'll know I don't like/trust Google. Instead of using Google to do your searches, check out www.duckduckgo.com. They don't track you or keep records of you and your searches.