As I paged through the documents, I couldn't find how long nor where files are stored during transfer. It kinda seems like they get stored (in encrypted form) in the guy's closet server.
(Disclaimer, I've not reviewed the code, don't quote)
Files can be transferred via P2P connection without them being uploaded first to a third location. I assume though that some sort of server serves as a matchmaker allowing two computers find each other when the connection is established
That's exactly what the relay server is, it just relays communication details. And you can run your own relay server if you don't want to use his public relay server.