Hi,
Since you get the contact emails logged in the backend of HikaShop, it means that HikaShop sends the emails to your email server so that he can send them. But your email server fails to send them.
And from what I can see in your screenshots, you're missing the "to" destination email address in the contact emails, which is probably why the email server is not able to send them.
That can happen if you emptied the field "from address" in your HikaShop configuration. So please make sure that you have your email address in there.