Probably want to develop a custom widget for the frontend if there's no user input. IF there is user input you'd want to develop a custom form.
https://docs.xperience.io/k12sp/developing-websites/page-builder-development/developing-widgets-in-mvc/example-developing-a-widget-in-mvc
https://docs.xperience.io/k12sp/developing-websites/form-builder-development/developing-form-components/example-developing-a-custom-form-component
For the admin API panel you described you'd want to develop a module
https://devnet.kentico.com/questions/create-custom-module-for-admin-ui
In terms of the actual API implementation, you'd use a seperate .cs file to call their API with HttpClient. The authentication can range from attaching a cookie to OAuth. This is pretty much the same across all C#/.NET. You'd call the API and return the data into the viewmodel.