In a server environment, the APIs should be set to the public URLs on which the apps are hosted.
The backend Admin UI app and API app and Payment API need to be exposed to the internet, so the UI's will be able to communicate with the backend without needing any special firewall rules.
They will communicate over the public URLs. This will correspond to the IIS binding for each app that exposes the app to the internet. While doing the initial setup, if HTTP is used (ie. SSL is initially skipped) then the port will be 80 by convention. Once SSL is configured, the apps will be hosted over HTTPS, and the port will be 443 by convention.
The API is responsible for managing the media (images), specifically the functionality to upload media from the Admin UI and the functionality to server media to the WebStore UI users.
The Payment API also facilitates handling payment info so that the Znode API can avoid that responsibility.