Hi,
I tried to check on the issue on your website but never received the activation email. It seems that there is a problem with the way you configured your email settings. I would recommend to check joomla configuration's and Hikashop configuration's emails settings with your hosting company.
Regarding the shipping methods not being displayed, I don't see anything in your screenshots which indicates a problem with what you did. Nevertheless, there has to be something done wrong. Maybe you modified the code some of the view files of HikaShop and mainly the "shipping" view file ?
If you could provide a backend access, we would be able to check on the settings and probably find the cause.