You would want to leave all the pages with the same structure as when you downloaded them, so you shouldn't be moving them around or you will affect some of the paths.
As long as your connection file is pointing to the correct database, you shouldn't have any problem with having any other tables in the database. It looks like the process that is being skipped is the insertion into the database. Is anything getting inserted into the database or is it not getting populated at all?
To check the insert query, find this line of code in the users_Registration_Simple.php file:
$WA_Sql = "INSERT INTO `" . $WA_table . "` (" . $insertParamsObj->WA_tableValues . ") VALUES (" . $insertParamsObj->WA_dbValues . ")";
After this line, add this line:
Then run through the registration again. Post back with what is displayed on the page.