The fate of dwarven souls is never made clear actually. They might actually die like men, or they might be more akin to elves, but without the ability to leave Valinor (dead elves can actually come back). Only when the elves started fighting with them (remember they started out super friendly with one another) did elves just start saying they disappear on death, which is against their own cosmology; anything Eru gave 'fea' too is eternal, in a sense. That is, an immortal soul. Which he totally gave dwarves.
And yeah, their bodies were crafted by Aule (who dwarves call Mahal), the Smith. They were more or less just puppets until he went to destroy them out of loyalty to Eru, but Eru gave them souls and showed Aule they were afraid of being destroyed; something Aule hadn't made them do. They had, at that point, will.
Oh, and hobbits are human. For the curious. That's not supposition or anything, they're descendants of the Edain, but they care so little about their own early history nobody knows how they came to be short, hairy footed midget-men.