Hi,
1. I would have said to disable it.
Note that in the "Display location" setting of the plugin, you can select either "web page", "popup" or "add to cart button". If you select "popup" there, you'll have a real popup in the center of the page.
If you select "web page", you'll have instead a notification box on the corner of the page, like on our demo website.
If you select "add to cart button", the notification box will be linked to the add to cart button.
So these are potential alternatives.
2. There is no option to disable that. However, you can add a bit of CSS if you want to hide it:
.edit_cart_product{ display:none; }
3. Create a menu item of the type "HikaShop checkout" via the Joomla menu manager, and select it in the "force a menu on checkout" setting under the Checkout tab of the HikaShop configuration and you'll be able to use the alias of the menu item to customize the URL of the checkout.