Hi,
First, I see that you're using the old checkout system of HikaShop 2. I would recommend turning off the "checkout legacy" setting of the HikaShop configuration in order to use the new checkout. It will make the checkout experience a whole lot better.
Regarding the registration, if you want to smooth it, you could deactivate the user account validation setting of the Joomla user manager options page. That way, the customers would be directly logged in after the registration, without having to click on a validation link.
Regarding the guest checkout, using the new checkout might help. Otherwise, we'll need to be able to reproduce the problem but I can see that the guest checkout is deactivated on your website so I couldn't look at the problem and so I'm not sure what is the problem.