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.
For the admin API panel you described you'd want to develop a module
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.