You don't need to modify the views for all that.
For the shipping address box, you can just edit the HikaShop CSS via the configuration in the tab display and remove the line float:left; from the code
.hikashop_checkout_address_right_part {
width: 350px;
float: left;
}
Don't forget to save the configuration once you did the modification and then clear your browser cache.
The address fields can be edited via the menu Display->Custom fields. You will be able to reorder them there as well.
The background of the popup is added by your template, you should tweak your template CSS for that.