Aragorn is not alone in his fighting skill. There are several Elf Lords that could best him in a heart beat. He learned his fighting skills from Elrond and sons...do you not think any of the three could best him if they wanted to?
By pure physical strength he could have bested Eowyn. But he also realized she would keep fighting. And any good warrior knows that someone who is willing to die for their beliefs is the worst enemy to come up against, because they will continue to fight until they are dead.
And yes so Frodo didn't toss the ring in, it was Gollum. So I suppose technically Gollum is the real hero.
