The signaling server is required to exchange messages between peers (SDP packets) until they have established a P2P connection.
A STUN server is there to help a peer discover information about its public IP and to open up firewall ports. The main problem this is solving is that a lot of devices are behind NAT routers within small private networks; NAT basically allows outgoing requests and their response, but blocks any other "unsolicited" incoming requests. You therefore have a Catch-22 scenario when both peers are behind a NAT router and could make an outgoing request, but have nowhere to send it to since the opposite peer doesn't expose anything to make a request to. STUN servers act as a temporary middleman to make requests to, which opens a port on the NAT device to allow the response to come back, which means there's now a known open port the other peer can use. It's a form of hole-punching.
A TURN server is a relay in a publicly accessible location, in case a P2P connection is impossible. There are still cases where hole-punching is unsuccessful, e.g. due to more restrictive firewalls. In those cases the two peers simply cannot talk 1-on-1 directly, and all their traffic is relayed through a TURN server. That's a 3rd party server that both peers can connect to unrestrictedly and that simply forwards data from one peer to the other. One popular implementation of a TURN server is coturn.
Yes, basically all those functions could be fulfilled by a single server, but they’re deliberately separated. The WebRTC specification has absolutely nothing to say about signaling servers, since the signaling mechanism is very unique to each application and could take many different forms. TURN is very bandwidth intensive and must usually be delegated to a larger server farm if you’re hoping to scale at all, so is impractical to mix in with any of the other two functions. So you end up with three separate components.
Regarding multi-peer connections: yes, you can set up a P2P group chat just fine. However, each peer will need to be connected to every other peer, so the number of connections and bandwidth per peer increases with each new peer. That’s probably going to work okay for 3 or 4 peers, but beyond that you may start to run into bandwidth and CPU limits of individual peers, especially if you’re doing decent quality video streaming.
