Reply To: the motherlode of confusion
The shader orb, probably has a UV Map added to it, but isn’t Unwrapped yet (hence the Square):
(I called it an empty UV Map, which probably isn’t quite correct, the main thing is, that it isn’t Unwrapped.)
The Material confusion, is, because you have one Material Selected, but the other Material is Assigned to it:
About the weird Unwraps, I am not sure, might have something to do with the Live Unwrap, but anyway, you should Add Seams to the model to get consistent and predictable results.