No problem, ask away :)
You could. Not sure what the use case would be...
But, the URLs for NuGet package versions are quite predictable, and you can discover them from the Download button in the UI. For example, the download URL for InedoLib v950.0.7 just looks like https://proget.inedo.com/nuget/NuGetLibraries/package/InedoLib/950.0.7
The NuGet API does not support Bearer authentication. You can specify an API key when publishing packages (X-NUGET-APIKEY header), and it might work when downloading packages? Haven't tested, and no one asked before. But you could also specify api:<apikey> as the basic auth credentials as well, so I guess that's really easy too.