How create a P2P web-chat without any server?

Malte Uble's excellent UniversalComet article does exactly that as a proof of concept. Even works with Iphone and Android phones.

Yes, but you must decide on a place to meet.

If your friend send his ip over to you, you can connect. Then you only need to tell some more people to join. After some time you will get bigger and bigger. Then, if some link on the net fail, the cloud will be broken up in two clouds(netsplit). Then everyone need to know how to get back to being "one cloud".

Some one in the cloud always have to play the server, that is done with voting. If all agreed on who is the server, then it's decided. If not agreed, shoot one down and vote again.

You have to host your own web-server to serve up the web-interface, I guess.

I have not tried this. But I think it would work.