IIRC, part of the reason Bilbo hadn't already handed the stone over was because he was afraid of Thorin's wrath for taking it in the first place. I may be remembering that wrong.

The other thing is that the reason Bard was so willing to fight is that he expected more Dwarves to come. Before too long, either the Dwarves would be able to counter-siege and force battle, or the Man/Elf alliance would be unable to keep them from pushing through to the Mountain without a pitched battle - at which point they'd have the dwarfpower to reopen other entrances and break the siege. Once that happened, Thorin would end negotiations.

The ability of Thorin and Company to meaningfully affect the battle isn't all that strange. There were only 13 of them, but they were equipped with the treasures of the Mountain (which included such grand weapons and armor that Bilbo's mithril shirt was little more than a trifle) and were attacking an undefended flank heading straight for the commander.