I have some questions, I guess Crazy Joe had too many ambitions, and he wanted to be the Don of the Profaci/Magliocco Family at that time, but he was believed to be a "hot headed" and he was used to act before thinking about a fact, he might make many mistakes, I don´t think he could be a good Don. How could Carlo Gambino back a guy like this?

It was more that Gambino was going against Joe Profaci than anything else. IF Gallo won then he'd have to swear allegiance to Gambino and would come under Don Carlo's thumb (much like Joe Columbo did a few years later)... even if Gallo DIDN'T win then Profaci would still have had a war on his hands.

It's not clear to me that the Gallos wanted to take over the Profaci family, or that Gambino backed them.
Their initial beef with Profaci, ca. 1960, was that Profaci didn't give them territories he promised them in return for whacking a guy who wouldn't pay tribute to Profaci. They kidnapped several high-ranking members of the Profaci hierarchy, but released them after the Commission ordered them to do so--and ordered Profaci to give them the territory he promised. When he welshed again, the war started up. I don't know that Gambino took sides at that point.
Later (ca. 1963-64), after Profaci died, Joe Magliocco took over. He and Joe Bonanno conspired to whack Gambino and Tommy Lucchese. Joe Columbo, a Profaci captain, betrayed the plot to Gambino. The Commission ordered Magliocco to pay a fine and step down--in favor of Columbo, not the Gallos.

He weltched? They were taking hostages! You wanted him to be fair with them? -- How can you be fair to animals? -- For Crissakes, listen -- They recruited sp*cs -- they recruited ni**ers -- and they did violence in their, in their Grandmother's neighborhoods. And everything with them was whores -- whores! babania -- junk dope! And they left the gambling to last.

Here we go again--more bulls**t parading as "knowledge":

--The Gallos did not want to be heads of the Profaci family. They wanted to be quasi-independent, operating the gambling rackets that Frankie "Shots" Abbatemarco had established in Profaci's territory without his approval. Profaci promised them the territories if they whacked Shots. They did, and he welshed (calling Frank Pentangeli!). That was the start of a long war whose immediate result was that the Gallos were no longer part of the Profaci family.

--Carlo Gambino and everyone else in the Mafia hierarchy regarded Joe Gallo as pazzo, and wouldn't touch him with a ten-foot pole--that's how he got his name. The idea that Gambino would have a tete-a-tete with Gallo as described above is beyond absurd.

--Gambino wanted Profaci, "the old man," to step down as Don in order to break up the alliance he had with Joe Bonanno. After Profaci died, the Commission refused to recognize his brother in law, Joe Magliocco, as his successor. Gambino encouraged Joe Columbo to undermine Magliocco from within. Columbo ratted out a plot that Mag and Bon cooked up to whack Gambino and Tommy Lucchese. Mag was forced to step down and Columbo, now Gambino's protege, was rewarded with the Donship.

--Meanwhile, Larry Gallo died of cancer, Joe went to prison for a long stretch on a vending machine rap, and Albert more or less disappeared. When Joe Gallo got out of prison, he approached Columbo, not Gambino, about receiving a share of the rackets that he'd originally disputed with Profaci. Columbo refused.

--Columbo had become a regular media star with his Italian-American Civil Rights League. His high profile angered Gambino. Columbo was shot and incapacitated at his Columbus Day rally in 1971. Many people at the time believed Gallo did it. Today, the consensus of most knowledgeable people is that Gambino ordered the shooting, but that Gallo didn't carry it out--Gambino just wanted people to think that he did. Carmine (the Snake) Persico was the major beneficiary of the shooting, not Gallo.

Sorry everyone, got this from a book. S.C tells me to look in different Mafia books, I do. But to get my hands on EVERY Mafia book is a little silly, no?

Not as silly as picking out a selection from just once source that appeals to you because it seems sensational--and posting it here as if you're the font of knowledge.

Mini, if you're really interested in the Mob, you should know that books about gangsters are notoriously unreliable. Gangsters aren't the kind of people who leave their collected letters and papers to university libraries so that scholars can study them. Many gangsters couldn't read or write--or if they could, they'd never leave reliable written testimony to their crimes. So, the people who try to make money by writing about them will usually print the most sensationalistic stuff--knowing that no one will be able to refute them. And the sensationalistic stuff gets picked up by other writers, so that one fiction gets repeated indefinitely.

That's why, if you really want to learn about the Mob, you have to spend time researching multiple sources--books, periodicals, and especially dozens of websites. Sooner or later, you'll acquire a feeling for what may be true inside all the bulls**t.