To the two points you raised:
1. The immigration scene was absolutely authentic. FFC, whose fanatical attention to detail shows everywhere in the GF Trilogy, nearly outdid himself in depicting Ellis Island (New York City), the entry point for most immigrants of that era. Even the part where Vito gets his last name is authentic: One of the agents says, "Vito Andolini from Corleone," and the chief guy says, "Vito Corleone." Many immigrants who couldn't speak or understand English had that experience. My family name was originally polysyllabic, but the immigration officer who processed my grandfather heard only the first syllable--and it's been that way ever since.
2. Immigrant and first-generation Italians often had difficulty in assimilating in America. One reason was that they suffered vicious discrimination--many bigots refused to even consider that they were "white." Another was the extreme insularity of southern Italians, who distrusted government and official institutions, including schools, police, etc. Opportunities were limited under those circumstances. The local Mafia boss was often respected because he could settle disputes and dispense "justice" without recourse to the police, the courts, or other institutions that the people didn't trust. For some, the Mafia became the "employer of last resort" because it offered opportunity and "respect." Keep in mind that we're talking about a tiny minority of Italian-Americans: at its peak, the US Mafia had only about 5,000 members. But the myth loomed (and still looms) large.