Yes, data is fragmented and served in chunks just like Bittorrent. You might only serve small chunks of any given piece of data, and as a downloader you may be downloading different chunks from different peers.

Are the chunks encrypted or obscured? That is, could an adversary with local access to the node determine what object a particular chunk is part of? How about an adversary that can see traffic, but not the node's storage?

They aren't, how would you encrypt them so the local user could read them but someone with local access couldn't? You'd have to ask the user for a password every time the service started up, which would be terrible UX.