Let's start with the first one:

[HttpGet("ExternalLogin/{provider}")]
public IActionResult ExternalLogin(string provider, string returnUrl = null)
{
    switch (provider.ToLower())
    {
        case "facebook":
            // case "google":
            // case "twitter":
            // todo: add all supported providers here

            // Redirect the request to the external provider.
            var redirectUrl = Url.Action(
                nameof(ExternalLoginCallback), 
                "Token", 
                new { returnUrl });
            var properties = 
                SignInManager.ConfigureExternalAuthenticationProperties(
                    provider, 
                    redirectUrl);
            return Challenge(properties, provider);
        default:
            // provider not supported
            return BadRequest(new {
                Error = String.Format("Provider '{0}' is not 
                                supported.", provider)
            });
    }
}

The code is quite straightforward. The first thing we're doing here is checking whether the given provider is among those supported by our application; if that's the case, we redirect the request to the external provider using a dedicated interface provided by the ASP.NET Core Identity authentication service; otherwise, we return a Bad Request.

It's worth noting that this controller won't be limited to Facebook; as a matter of fact, it will act as a common interface to deal with (almost) any external provider we might like to add in the future, as long as it's supported by ASP.NET Core.