Hi,
The link you provided doesn't have HikaShop:
monosnap.com/file/xv1ex9QsWDVfTiNN1nHevjJkOsXYhM
Regarding the white border, you need to change the setting with the same name but in the edition page of your menu item in the Joomla menu manager. The setting in the HikaShop configuration is the "default" setting for new menu items but it won't change for existing ones.
Regarding the proceed to checkout button, this means that you've set the "Force SSL on checkout" setting of the HikaShop configuration to "shared URL" with a wrong URL.
I would recommend leaving that setting turned off.
If you want SSL on your website, you need to first setup a SSL certificate for your domain name, and then activate the "force SSL" setting of the Joomla configuration so that it is activated on the whole website. It will also help your SEO.