Hi,
1.
The border of the inputs is removed by the CSS of your Joomla template. So you'll have to modify somehow the CSS of your Joomla template to add back the inputs border, like it is by default.
I would recommend you to contact your template provider for help on how to do that as it depends on how your template is made.
2.
For the main fields, you have the setting "registration" of the Checkout tab of the HikaShop configuration.
For the address fields, you can go in the menu Display>Custom fields.