YouTube live on iOS?
Streaming from an iOS device is no different than streaming from any other device. You would have to write an h264 encoder and RTMP packetizer, and send the video to your YouTube stream object's ingestionAddress. Outlining the details of the encoder beyond the above is too broad for Stack Overflow, but I highly recommend looking at the VideoCore iOS project.
As far as branding goes, the only way to play back YouTube content in an iOS app without breaking YouTube's terms of service is to play the video in a UIWebView or YouTube's iOS player helper library (which is just a web view with some playback interfaces).
There is no way to completely remove YouTube branding from the IFrame player. However, there are branding options you can toggle using the modestBranding flag on the player. See the IFrame docs here.