Why are the men and elves armed as if for war? Why did they come as a great host, instead of sending scouts well ahead? Why not send birds as scouts, since apparently birds can talk? Why not a swift boat?
News of Smaug's death had spread far and wide. They were probably armed against other potential rivals such as goblins and bands of human bandits. Why a host? Safety in numbers. Perhaps most birds are unreliable scouts, easily distracted by food, shiny objects, etc.; few Men outside of the descendants of Dale seem to have picked up the knack for understanding bird-speech. Close to the mountain, the river might not be suitable for boats.
Why did not the men and elves answer Thorin? Why didn't they come back that day? Why move the camp between the arms of the Mountain?
The scouts were doubtless surprised to discover Thorin and his companions alive. They returned to the camp to report, resulting in the moving and consolodation of the camp.
What do the younger dwarves mean when they wish "things had fallen out otherwise"? Under what conditions would the dwarves have welcomed such folk as friends? Why do the younger dwarves in particular have this reaction?
The younger Dwarves are probably less set in their ways and perhaps more appreciative of the help that they obtained from the humans of Lake-town. They may also be less accustomed to hardships then the more senior Dwarves and may miss the comforts and welcome provided by the people of Esgaroth.
What is missing from this song? What or who does it fail to mention? Who composed this song and why? Is this how they felt, or were they trying to make Thorin happy?
Compare and contrast it to the dwarves's song at Bag End
Missing? Specific mention of the Arkenstone? I'm not sure what you are getting at. No mention of Bilbo or burglars, but the song may have been composed before, and in anticipation of, the Mountain-king's return. It might be a bit much to assume that it was composed on the fly by Thorin's companions. I'm sure, though, that they did mean to cheer Thorin up, as well as invigorate their own spirits. The new song does seem to be a companion piece to the one sung at Bag End; maybe they were composed by the same Dwarven skald.
Is there anything Bard could have done to handle this more diplomatically? Could he have sent the elves away? Heck, could he have sent all but a token force away while they parleyed? Why did he not do so? Why did not Gandalf get involved? Did Bard or the Elvenkind know that there were more dwarves a few days away? Did they have any idea that goblins might show up? Did they know what they were getting into? How could they be so ignorant?
Dwarves seem very serious-minded. Bard's approach was probably as good as any. Bard had no authority over the Elves; he could only have sent them away with the Elvenking's co-operation. Gandalf is probably taking a wait-and-see attitude at this time to assess Thorin's behavior. We know that he does involve himself later. The Men and Elves are not yet aware of the approach of Dain's folk, although as locals they should be well-aware of the existance of the colony. They came as a host (or hosts) because they were aware of the possibility of goblins; I doubt, though, that they were expecting an entire army of them. They simply did not have any intel yet on the movement of Dain's forces, not knowing that the colony of ravens that could converse in the common-tongue still existed at Erebor.
Bard was the spokesman, but could the Master of Lake-town have done a better job? Is not he less blunt, and more political? How might he have dealt with the dwarves in a more effective way? Flattery, perhaps? Some promise of trade or transport or food? Perhaps asking for a private word, and then confessing that he doesn't trust the Elvenking either?
The Master remained behind, so there is no way to know how Thorin would have reacted to him. But since the dragon-sickness had come upon Thorin, who had also sent for Dain, I don't think that the Master would have had much better success. Still, trying to convince Thorin that the Men could become allies against the Wood-elves might have been an interesting approach.
How did they come up with one twelfth? Bard seems very firmly in charge, and is getting handsomely rewarded. Is that fair? After all, he was in the Laketown army. Other people shot at Smaug; he happened to hit. Why should he get all the credit and all the reward? A reward, sure, but all of the reward and then personally donate, if he so chooses, to Laketown? How does anyone know he is the heir of Girion? What does that even mean, so many generations later?
What is the Elvenking getting out of this? Why donft any of the elves have anything to say to the dwarves? Might a well-worded apology be in order?
A share of one-twelth may have just seemed like a good place to begin negotiations. Bard has his own ideas, now, of restoring Dale. That is going to be expensive and he knows it. Other Lake-town residents are also descended from Dale; they would have kept at least some of the old stories and history alive. Indeed, Bard is probably counting on many of them for help. The demand specifically calls for Bard donating a portion of his share for the relief of Lake-town.
Thranduil proabaly realizes that adding his own demands is not a wise idea at this time. An apology for the Dwarves' treatment might be a good idea, but I suspect that the Elvenking has his own pride and balks at apologizing for what he saw as a necessary precaution. At this point, it seems as if Thranduil regrets the idea of marching on Lonely Mountain and has given up on the idea of receiving a share of the wealth from the Dwarves.
What does dragon stink smell like? Do dragons poop, and if so, where?
Why are Bombur and Fili and Kili less happy with Thorin than the other dwarves? Why does not Bilbo say something? Was not he almost leading this party for a while? Couldn't he at least try?
Any other comments on any part of the chapter?
I really don't want to speculate on the odor of dragon crap, but I imagine that Smaug had a special area for doing his business (unless he only shat outdoors while airborne).
Bombur may remember all of the great food that he enjoyed while staying in Lake-town (as opposed to the dwindling supply of cram that they were eating now). Fili and Kili are the youngest Dwarves in the company and are possibly the most open-minded. Bilbo seems to have gained enough wisdom to know not to antagonize Thorin at this time. His time is coming in the next chapter, but he has to formulate a plan first.
'There are older and fouler things than Orcs in the deep places of the world.' - Gandalf the Grey, The Fellowship of the Ring