All these CSS modifications can be done via the CSS edition interface in the Display tab of the configuration ("Hikashop->System->Configuration->Display"):

How to move the registration box below the login box on the checkout

You need to edit the CSS of HikaShop via the interface in the configuration under the tab display in the CSS area and change the code:
.hikashop_checkout_login_right_part {
  1. width440px;
  2. floatleft;
}
to:
.hikashop_checkout_login_right_part {
  1. width440px;
}

 

How to move the shipping address selection box below the billing address selection box on the checkout

You need to edit the CSS of HikaShop via the interface in the configuration under the tab display in the CSS area and change the code:
.hikashop_checkout_address_right_part {
  1. width350px;
  2. floatleft;
}
to:
.hikashop_checkout_address_right_part {
  1. width350px;
}

 

How to change the color/size of the prices in HikaShop

You need to edit the CSS of HikaShop via the interface in the configuration under the tab display in the CSS area and modify the code:
span.hikashop_product_price {
  1. color: #900;
  2. white-spacenowrap;
}

 

The text of some buttons in HikaShop doesn't fit in the styling of the button

The styling of HikaShop buttons is handled by default by your template. If the text doesn't fit in the styling, that's because the template you're using uses a static styling for the buttons with a fix width. So, you have three solutions:
  1. You change the styling of buttons in your template so that it works regardless of the text in it. You might want to contact your template provider for that.
  2. Change (shorten) the text of the buttons so that it fits the styling. You can do that via the interface in the configuration under the tab languages.
  3. Change the option "button style" from "normal" to "css" in the tab "Display" of the configuration of HikaShop so that it uses HikaShop's default CSS for the buttons instead of your template CSS. You will then be able to edit the CSS used by the buttons by editing the CSS of HikaShop via the interface in the configuration under the tab display in the CSS area
 

How to hide some parts of the pagination ?

You need to edit the CSS of HikaShop via the interface in the configuration under the tab display in the CSS area.
There, in order to remove the number of items per page selection (with the dropdown), you can add the CSS:
.hikashop_products_pagination div.limit, .hikashop_subcategories_pagination div.limit{ display:none; }
In order to remove the results counter text below it, you can add the CSS:
span.hikashop_results_counter{ display:none; }

How to display the product code on the product page ?

You need to edit the CSS of HikaShop via the interface in the configuration under the tab display in the CSS area.
There, in order to display the product code on the product page, you can remove the CSS:
.hikashop_product_code_main{ display:none; }

How to change the border around products and categories on listings ?

You need to edit the CSS of HikaShop via the interface in the configuration under the tab display in the CSS area.
There,  you can change the CSS:
div.hikashop_products div.hikashop_subcontainer{
border: 1px solid;
}

How to change the size of the small thumbnails on the product page (you see them only when you have several images attached to a product) ?

You need to edit the CSS of HikaShop via the interface in the configuration under the tab display in the CSS area.
There,  you can change the CSS:
div#hikashop_product_left_part img.hikashop_child_image{
margin : 2px;
height:25px;
}

How to hide the characteristic values in the product name on the product page ?

You need to edit the CSS of HikaShop via the interface in the configuration under the tab display in the CSS area.
There,  you can change the CSS:
.hikashop_product_page .hikashop_product_variant_subname{
display: none;
}

How display the characteristics radio selection vertically ?

You need to edit the CSS of HikaShop via the interface in the configuration under the tab display in the CSS area.
There,  you can change the CSS:
.hikashop_product_characteristics_table{
width: 100%;
}
.hikashop_product_characteristics_table input{
float: left;
clear: both;
}
.hikashop_product_characteristics_table label{
display: block;
}