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At the end, Hawkeye holds the other Hurons at bay with his rifle so that Chingachgook can fight Magua. But if you pay close attention, you'll notice that he never had time to reload his rifle... meaning he threatened the Hurons with an empty gun. It works.
He did pick up a rifle from one of the Huron they shot along the way. Did he already fire it before then?
He does, taking out one Huron with it right before going into the standoff with the empty rifle. In fact, doing so likely helps his bluff.
Magua's reaching out to Alice may have been a cynical ploy to show that he "tried" to save her. He clearly did not want to marry her as per the command of Sachem but if she died of her own free will, who can blame him?
He certainly doesn't try to catch her before she falls, and the other Huron don't stop her from going near the ledge.
Additional Fridge Brilliance: She joins her lover at the bottom of the chasm. Together in death...