public abstract Connector GetConnector()

Layer selectedLayer = MapView.Active.GetSelectedLayers()[0];

if (selectedLayer is FeatureLayer)
{
    FeatureLayer featureLayer = selectedLayer as FeatureLayer;

    using (Table table = featureLayer.GetTable())
    using (Datastore datastore = table.GetDatastore())
    {
        ServiceConnectionProperties serviceConnectionProperties = datastore.GetConnector() as ServiceConnectionProperties;

        if (serviceConnectionProperties == null)
            return;

        Uri url = serviceConnectionProperties.URL;      // Will be the URL to the Feature Service.
        string user = serviceConnectionProperties.User;     // The username property will only be
                                                                                                                // populated for feature service hosted
                                                                                                                // on non-federated ArcGIS Server.
        string password = serviceConnectionProperties.Password; // Will always be empty.
    }
}