The price didn't appear doubled when I tried.
What product did you add? What was the price, what price did you expect?
You had some issues on your login and forgot password pages that I addressed, and I added the usergroup session variable to the login page. Now you can just add the security assist rule to check its value.
The results page doesn't add to the cart or redirect, because you haven't applied the add to cart server behavior on the page.