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Yeah, it's initial peer discovery and connection setup (if behind NAT) I'm talking about. Once you've found the other PC and got a connection set up then all is well ;-)

Do these services also act as connectors in case of double NAT?

STUN allows all sorts of hole-punching for cases where both peers are behind NATs. For cases where the hole-punching doesn't work (a user behind two NATs might be one case), you can use TURN which is a dumb UDP or TCP relay.

They certainly can, I don't know if they do in practice. It always work for me, so I haven't investigated too much.

Which is a step backwards compared to bittorrent, since that can also provide decentralized hole punching, bootstrapping and peer discovery and not just the bulk data transfer. Plus being implemented at the TCP/UDP level allows more fine-grained control over the data flow, making it more friendly towards the network.

They're also needed for the actual javascript code that runs everything.