I just looked at inquiry.php so far, but I imagine the others are the same.
The captcha is passing ?field=Security_Code_2
but the validation is still checking: $_SESSION["captcha_Security_Code"]
I'll bet that editing the design is incrementing the field name and that is causing the problem. The solution is to make sure they match, so either update the field name in the captcha image or the session name in the validation to make sure they are referring to the same value.
I'll take a look at the extension and see if updating the design updates the captcha field name and get that corrected if that is the case.