Hello,
1.
Regarding your shipping method which isn't showing, following each step of the "shipping methods" section of the FAQ will probably help you :
www.hikashop.com/support/faq.html#ship
2.
I just tested it through your website, and it seems like you can't go through the last step of your checkout workflow because "no shipping method was found", so you should firstly fix your shipping issue.
Also, you don't have any error message displayed through your checkout workflow, reading that
thread
will probably help you :
HikaShop uses the core Joomla messaging system to display messages on your website so if you don't see any message when you don't enter correct information during the checkout process, that's probably because your Joomla template does not contain the tag to display Joomla messages: <jdoc:include type="message" />