I understand that it misses part of the WebRTC concept of peer to peer, but in case I want to be sure I overcome any network issues, would it be possible to stream all videos through the server instead of between the peers?
If so, would it duplicate the number of connections as well or is it possible to stream all videos from the server on one socket?
That is exactly what Licode does. There is a central server, the MCU, that acts as the central point of a network with star topology. You only send your video once and it gets streamed to every subscriber.
Not sure about the sockets part. AFAIK, right now you have to open a new connection per subscribed stream, but there was a PR discussing multiplexing all streams in a single Ice connection. @Javier can give you more info on this.