1. I go with Carlo Gambino because he made the family the most powerful in the nation. His predecessor, Albert Anastasia, had tremendous personal force and was greatly feared, but his wasn't the most powerful family. And, at the end of the day, he was assassinated, while Gambino died peacefully in his own bed.
2. There may have been some dissent after Gambino took over. But within a month, Gambino's main supporter, Vito Genovese, called the famous Apalachin convention, which was held (among other reasons) to anoint and legitimize Gambino.
3. Gotti's main reason for planning Castellano's assassination was self-defense. After Gotti's patron and protector, Aniello (Mr. Neil) Dellacroce, died, Castellano announced that he was breaking up Mr. Neil's crews, which included Gotti's crew. He also announced that his new underboss would be his chauffer, Tommy Bilotti, a stammering, bat-wielding thug whose only qualification was his loyalty to Big Paul. So, when Castellano called Gotti to have dinner at Sparks that night, Gotti had reason to think it might have been his Last Supper, so to speak.
But Gotti probably wouldn't have moved against Big Paul if he didn't think he'd have the support of others in the Gambino family. He did have support--not because others loved Gotti, but because they hated Castellano. He was a penny-pinching cheapskate who squeezed his people unmercifully and micromanaged the family. He was a near-recluse who seldom left his Staten Island mansion to mingle with the guys. He also committed two unpardonable breaches of Mafia "etiquette": He failed to attend Mr.Neil's wake and funeral, and he carried on openly with his Colombian-born housekeeper under his own roof, with his wife and daughter present.
BofB, much has been written about Castellano's alleged objection to dope-dealing. I don't think that was a major factor in the Gotti-Castellano feud. Big Paul's wrath was aimed at Angelo (Quack-Quack) Ruggiero, whose dope-dealing was caught on law enforcement tapes--and the tapes potentially were damaging to Castellano. He demanded to have copies of the tapes, but Mr. Neil stalled him. Then the Feds filed a RICO charge against Castellano, and he had bigger things to worry about.