1. What was the name of the first boss that lead what was knwon to be the Luchese Family? What happened to him?

2. Who was the most powerful Don that ruled the Luchese Family?

3. Of the 5 Families, were the Luchese the ones who were involved in the Garment industry more than the other four?

4. I heard somewhere that the daughter of a Luchese family member married the son of a Gambino Family member, thus, an allaince is born.

This story gets a little complicated by the famous Castellemmarese war:
The origin of the Lucchese family goes back to Tom Reina, who sympathized with Salvatore Maranzano. This news got back to Maranzano's rival, Joe the Boss Masseria, who had his triggerman Peter the Clutching Hand Morello murder Reina. To compress a long story: after the war ended with Masseria's victory, he named Gaetano Gagliano as boss, with Tommy Lucchese as underboss. Gagliano ruled until 1953, when he died of natural causes and Lucchese took over. Lucchese was the most powerful and influential boss in that family.
Carlo Gambino, a clever and shrewd man, always believed in blood and marital ties. His cousins, the Castellanos, arranged for him to come to America. In turn, he named his cousin Paul Castellano as his successor. But, before that, his son Tommy married Lucchese's daughter. That marriage healed a previous rift between the two dons. It also gave Gambino access to the Idlewild (later Kennedy) Airport hijacking business, which Lucchese controlled.
The garment rackets were created by Louis (Lepke) Bucholter, the wealthiest and most powerful organized crime boss of the Thirties. But Lepke, who ran Murder Inc., was forced into hiding when one of his underlings ratted him out. Lepke eventually surrendered to the FBI, and was later prosecuted by Thomas Dewey, who sent him to the chair in 1944. After he surrendered, his pal Albert Anastasia took over the garment rackets, which stayed with Anastasia's successor, Carlo Gambino. Lucchese had his own trucking rackets in the garment center, which passed to his son in law, Tommy Gambino, after he died in 1967. Tommy ran those rackets for Castellano and Gotti until Tommy was prosecuted and convicted in the Nineties.

To get an idea how the Lucchese family controlled the airport hijacking business, watch Goodfellas. Tommy, Jimmy, and Henry were part of Paulie's crew, and Paulie was a Capo in the Lucchese family.

Tommy, three finger Brown, Lucchese was the big boss of that family.

I've always felt he was the prime mover in the Genovese-Lucchese-Gambino alliance that allowed Carlo to take control of the commsion.