Hi,
The changes you make in Display->Views are always done only for one template. If you sometimes don't see the modification, it's likely to be because you edited the view for another template than the one you're using.
When you add a new template, an easy way to put all your view modifications to that new template is to copy from your current template folder templates/YOUR_TEMPLATE/html/com_hikashop to the same location in your new template. You can do that view FTP.
For the reordering of shipping methods, that's something which has been corrected in the latest version of HikaShop. The problem won't occur if you update.