Its possible, but not with Twitch. You need low latency (encoding + transport). You can use FFmpeg + x264 with zerolatency tune for encoding. Nginx for own rtmp serwer. You may use diffrent protocol than rtmp and then you can also use low latency audio codec like Opus (similiar to codec used by Skype). On iphone you can connect and watch it. These is just for watching, for inputs there is another work. I think its just too hard for beginners, but not so hard if you get some skills. Another question is if delay wouldnt be too high. 500 ms delay or lower should be possible.
Here is nice read about latency in x264 made by dev of x264 http://x264dev.multimedia.cx/archives/249