Popup issues

I am using Joomla 1.7, Joomlavi Framework with the Melody template and the latest Hika Shop Version.

If I add an item e.g. 1.gigs.at/online-shop/product/cid-205 to the cart, the popup opens and it seems there is no CSS attached to the popup and there is no "continue shopping" button. If I click on the checkout button the checkout process (whole page) opens in the popup window.

If I use the cart checkout button and then click on "Please accept the terms and conditions before proceeding" instead of terms the cart items pop up...

I know its an issue with the template, but maybe someone already had the same issues and can help me to fix that problem(s).

The problem indeed seems to be in your template.
The popup uses the link:
1.gigs.at/online-shop/checkout/notice/tmpl-component
The /tmpl-component part of the URL tells joomla to use the component.php file of the template instead of the index.php file of the template so that only the main area is displayed. If you remove that part of the URL, you will see the same page inside the template. So the URL becomes:
1.gigs.at/online-shop/checkout/notice
As you can see, it displays the popup notice inside the template.

So in conclusion, there seems to be a problem with the component.php file of the template which tries to display the module instead of the content area. I don't know why though.
I suppose that if you use another template it works correctly right ?