1. Barzini didn't "break the peace." The agreement the Dons made with Vito was that the war would end, no attempts would be made on Michael's life in his return from Sicily, and Vito would provide police/political protection for the drugs trade in the East. Period. Barzini horning in on Tessio's territory wasn't part of that agreement.
I think "the peace" had to include such things as respecting one another's territories and not shooting any more police captains. In the book, at least, Vito had forged a nationwide "agreement to enforce peace in the underworld," that particularly included territorial integrity. I can't imagine that the peace conference was intended to rescind that.
