Twitch is not using P2P. This can be checked by accessing a live video on their site (the flash plugin does not prompt to request P2P access as when using rtmFp).
Video is published to a rtmp address (relay server) and then played back from there. Probably using Wowza Streaming Engine.
P2P RTMFP (often used by chatroulette type sites) and is less reliable than RTMP relay server. It's highly dependant on user ISP and network settings. From our tests users with regular internet connection often have huge latency or can't stream video at all when trying to connect using rtmfp to somebody outside their network.
Screen sharing is possible with external tools that simulate webcam from desktop:
http://www.videochat-scripts.com/scr...chat-software/