I wasn't sure how Vito knew it was Barzini (still might not be totally sure)
Most here would agree that it was Barzini's dominance at the "Big Meeting". He took the leadership role in summarizing the agreement on the narcotics issue. Vito saw that as Barizini muscling in on the action and thus muscling the Corleone's out.
Ditto. This is why I posted above that when (in this case) watching a film one has to draw on one's life experience to interpret scenes. That takes a certain amount of experience with life, being in different situations, one's capacity to infer from speech and behavior, and exercise of judgement.
