I think Balin was the oldest, but not 100% sure. As for killing Smaug - well, the whole book is littered with cheery references like Gandalf's telling the Dwarves that he doesn't really expect to see them again after they enter Mirkwood and how unlikely it is that they'll ever get there; granted that Gandalf is presented as a (somewhat) less serious sort of wizard here, there's still a strong feeling that for the Dwarves it's all about the journey and not about the end. They don't seem to know themselves what they'll do when they get there, even Thorin is so consumed by his desire for vengeance on the creature that destroyed his ancestral home that he doesn't think things through very practically.
Witness the Dwarves' behavior once they reach the Mountain. Then don't really seem to know where to go from there. They're brave, but not exactly full of forethought. They go up to the "doorstep", and Bilbo is the one who has to point it out to them when the keyhole appears. Bilbo goes down and gets the cup, and they are rejoice and then get rather cranky with him for not being able to do more, as if one hobbit could. And the Dwarves are weirdly passive throughout the last adventures; they never even seem to think of making plans for sneaking in and killing Smaug while he's asleep, for example. And once he leaves the mountain they're locked up inside (not their fault, really) until the whole show with Bard is over and the dragon is dead, thus conveniently solving their problem. And even THEN all Thorin can do is sit on top of his newfound pile and refuse to treat with the others who want a share of it. He can't see twenty-four hours into the future, once the Mountain is reached.
As for what they would have done if Smaug had not fortuitously decided to fly out over town and expose himself, who's to say. Thorin may well have sent for Dain to help him out; it's easier to see Dain being enlisted than the Lake-men. But how to kill the dragon who insists on staying inside his treasure-trove, the only think I can think of is a sneak attack while he's asleep - or awake, if they really want to kill themselves - or luring him out and then shooting at the weak spot Bilbo saw, and the Dwarves don't seem to be great ones for archery.
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Father, dear Father, if you see fit, We'll send my love to college for one year yet
Tie blue ribbons all about his head, To let the ladies know that he's married.
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