That should work fine. In contrast to what you might expect, Unity has no "root node" which you can ask for its children. You have to do what you do now.

GameObject doesn't actually contain a definition for FindSceneObjectsOfType(). You'll want to use

Type[] myVar = FindObjectsOfType (typeof(Type))

instead. For all GameObjects it's just

object[] obj = GameObject.FindObjectsOfType(typeof (GameObject));
  foreach (object o in obj)
  {
       GameObject g = (GameObject) o;
       Debug.Log(g.name);
  }

The SceneDumper script on the wiki will iterate all the the selected objects and their children. Currently it just prints the object hierarchy and the names of each object's components, but it could be modified to print all the component properties, filter by type, etc.

Given a game object, you can find its top-most ancestor in the scene tree using Transform.root -- i.e. gameobj.transform.root.gameObject. But note that there can be multiple "root" nodes in a scene.

And what must I do if I want to get ALL the objects of a given type, not only the ACTIVE ones?