1) No.
2) Capture card, second PC, then game source should become 'Video Capture Device' and you'll get couple of other problems (read the forum:).
3) Buy other webcam (actually, almost each game designed to have good feedback, low latency).
4) Don't use webcam in streaming. Record it separately and sync it in post-processing task.
There was a thread about it:
Webcam help?