Adding a survey at checkout

Is there a way to add a custom survey with checkboxes during checkout process by adding the required custom fields? Or would this have to be completely a custom script inserted in the checkout process?

You can use custom order fields for that indeed. You can see an example on our demo website where we ask the user for additional information. The textarea there was created with a custom order field.
Custom order fields are only available in the Business edition of HikaShop.

I installed the business addition and added my custom field. It is several radio buttons, and they format so close to each other that you can't tell what word goes with what radio button. I would like to stack the radio buttons vertically to fix this issue. How can you format the display of the custom field radio buttons?

You should be able to do that with some CSS.
If you give a link to our website store, we could give you more precise directions.

Here is a link to one of the product categories to add an item to the cart. Additional info is at very bottom of the cart. abet.securetesting4.info/index.php/products/s4000-model

You can add the CSS below via the CSS edition interface in the config under the tab display:

#hikashop_checkout_additional_info input { float: left; }
#hikashop_checkout_additional_info label { dispay: block; }