Did the organised crime community..?

But I recall it's something like five or so years between Vito's passing and the killing of the Don's of the NY families.

No. It was almost immediately. Vito had cautioned Michael that someone he trusted would approach him about a meeting with Barzini and whoever proposed this meeting would be a traitor because Michael would be killed at said meeting.

At Vito's funeral, Tessio approached Michael. So the meeting was to take place soon after, except Michael had the heads of the families killed before it could happen.


Would they have assumed it was all Michaels doing or that it was Vito's power play?

Vito swore that he would not break the peace and he kept his word. The other families would have to believe that it was Michael. There would probably be the supposition that Vito counseled him but, strictly speaking, it was Michael's doing. Vito was dead. Michael was now in charge.


Could they have integrated members of the Corleone's into the foundations of the other families and had them work their way up in that space of time to try and get close, especially with Barzini and Tattaglia?

Why would they? They were at peace. The other heads of the families were visible enough that they could be easily killed. Besides, as previously mentioned, there was no, "space of time."

When Vito swore that he wouldn't break the peace. He obviously meant during his lifetime. Whatever happened after that was fair game.

We know that at least some mob leaders didn't ask who have the order, because it was business and that was the business they had chosen.

This is one area where the deviation from the book did not improve the movie, storywise, though it made for a more dramatic scene. The other four families will absolutely know Michael ordered it. His being the only Don who survives will ensure that.

As I said, the assassinations of the heads of all four of the other families is an iconic scene, and makes for great drama, but from a strategic standpoint, it really makes no sense -- the other four heads will all have successors ready to take the place of the murdered leaders. By killing all the other dons, Michael is declaring war on all four of the other families, and doing so at a time when Tessio's regime is compromised, and possibly untrustworthy.

This is why, in the novel, Michael only had Barzini and Tattaglia killed (along with Moe Greene out there in Vegas, just as in the movie). From a story point of view, that makes a whole lot more sense: it leaves the Stracci and Cuneo families neutral, and having no reason to oppose the Corleones. By assassinating Don Stracci and Don Cuneo, Michael would force their families into alliance with the Barzini and Tattaglia families. By leaving them alone, however, Michael simultaneously gives them no cassus belli, and can then point to the fate of Barzini and Tattaglia as a warning to Don Stracci and Don Cuneo not to tangle with the Corleone family. This actually makes the Stracci and Cuneo families more likely to put pressure on Barzini's and Tattaglia's successors to end the war -- both sides have taken losses, Michael had legitimate grievances after the attempt on his father's and his lives, and the murder of Sonny. Time to end the fighting so they can all get back to doing business. None of that works if Michael goes after everybody.