I don't know what it is about the horrid song that makes it stick in my head,
but it does!
1.) Aragorn does all of this because he's Aragorn. Tolkien gives
heredity (I think) a sentimental nod in that Aragorn is Elendil's and Isildur's
heir and could not have done this without being their heir; but there is no
guarantee that Arador or Arathorn could have done what Aragorn did just
because they too were descended from Isildur. The two things come
together.
I would say that nothing of this is pre-determined in any
way. Aragorn has free will in all of this: he can fail; he can make other
choices.
2.) You could say, with the Rohirrim:
"Where will wants not, a way opens."
Don't forget, several hundred (thousand?) dead were compelled by that will
also. This is what leadership is all about.
Aragorn doesn't have a choice. He looked into the
palantír with the intention of forcing Sauron's hand; and now he has to deal
with Sauron's hasty stroke. Aragorn doesn't want to take the Paths of the
Dead. He has no sure knowledge how things will turn out, but this is the
only way. So, my answer invokes neither desperation nor confidence, but
rather
necessity.
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All that is gold does not glitter,
Not all those who wander are lost;
The old that is strong does not wither,
Deep roots are not reached by the frost.
From the ashes a fire shall be woken,
A light from the shadows shall spring;
Renewed shall be blade that was broken,
The crownless again shall be king.
