We laugh about Rankin Bass - but you must admit the songs are catchy!  (Like advertising jingles!)
2) I think it is Aragorn's resolve combined with his men's/elves/dwarves confidence in his ability that is important here.  You need both to be successful.

1) This is a more complex question.  Probably other heirs to Isildur could have called on the dead to fulfill their oath and fight with Sauron - but they didn't.  So it is Aragorn's genetics, the timing of it being Aragorn fighting Sauron in the Third Age, and, most importantly, Aragorn himself.  Aragorn makes many choices that show he is right for the Kingship- mostly by his turning away from the obvious path to CLAIM the Kingship and taking the more dangerous road to EARN the Kingship.  (Now I am thinking of Robert Frost - two roads diverged in a yellow wood....)NZ Strider has talked about this in several of his posts - I think he references this point in one of his posts earlier in the chapter. So it is the combination of who he is as well as all his life choices making him what he is that allows Aragorn to call the dead.