This is a bug of your RocketTheme template which doesn't handle properly the styling of the checkboxes with IE. Please deactivate that option of your template and it will work, it's not a problem in HikaShop or SSL.
Regarding the order not being confirmed, I would need more information on the problem. Do you receive other emails from your website (if not it means that the problem is with your email server, not in HikaShop) ? Are your orders status confirmed ( if not it means that the issue is with your server or another extension blocking the payment notifications to HikaShop) ? Did you deactivate some of the emails via the menu System>Emails (if yes, then maybe you want to activate them back) ?