Hi there!
Are you using Paypal Express? If so, the Paypal button or checkout button will take you from the checkout page to Paypal's page where your customers will then input their data (billing & shipping address, credit card info etc). The next screen is where your customers will input their discount codes and select their shipping options. They will then confirm the total and their account will get charged. Try a transaction yourself on your store and refund yourself afterwards :)
You'll definitely see the discount codes and shipping options.
I hope that helps!