public IReadOnlyList<Favorite> GetFavorites()

var favorites = FavoritesManager.Current.GetFavorites();
foreach (var favorite in favorites)
{
  bool isAddedToAllProjects = favorite.IsAddedToAllNewProjects;
  // retrieve the underlying item of the favorite
  Item item = favorite.Item;

  // Item properties
  var itemType = item.TypeID;
  var path = item.Path;

  // if it's a folder item
  if (item is FolderConnectionProjectItem)
  {
  }
  // if it's a goedatabase item
  else if (item is GDBProjectItem)
  {
  }
  // else 
}

var favorites = FavoritesManager.Current.GetFavorites();
foreach (var favorite in favorites)
  FavoritesManager.Current.RemoveFavorite(favorite.Item);

ArcGIS.Desktop.Core.Events.FavoritesChangedEvent.Subscribe((args) =>
{
  // favorites have changed
  int count = FavoritesManager.Current.GetFavorites().Count;
});