2 things...

1) After Vito calls a meeting with the heads of the five families to reason together and make peace, he tells Tom that he didn't know until that day that it was Barzini, not Tattaglia, that killed Sonny. How did he know this exactly?

2) Along with that, the scene where Michael and his father are talking in the garden, and Vito is telling Michael that someone in the family will betray him and will set up his assassination...How did Vito know that Barzini was gonna try to kill Michael? (Especially after Vito agreed to put up political protection for the drug rackets, and they had made peace.) Did Barzini sense that Michael did not share his father's sentiment about not breaking the peace they made? Could someone clear this up?