Michael: My father is no different than any powerful man, any man with power, like a president or senator.
Kay Adams: Do you know how naive you sound, Michael? Presidents and senators don't have men killed.
Michael: Oh. Who's being naive, Kay?
Tom Hagen: I'm an attorney for the Corleone family. These men are private detectives hired to protect Vito Corleone. They are licensed to carry firearms. If you interfere you'll have to appear before a judge in the morning and show cause.
Clemenza: Leave the gun. Take the cannoli.
Michael Corleone: Fredo, you're my older brother and I love you. But don't ever take sides against the Family again. Ever.
Don Corleone: You talk about vengeance. Is vengeance going to bring your son back to you? Or my boy to me?
Sonny: What the hell is this?
Clemenza: It's a Sicilian message. It means Luca Brasi sleeps with the fishes.
Calo: In Sicily, women are more dangerous than shotguns.
Sonny: Goddamn FBI don't respect nothin'.
Michael Corleone: It's not personal, Sonny. It's strictly business.
Clemenza: Mikey, why don't you tell that nice girl you love her? I love you with all-a my heart, if I don't see-a you again soon, I'm-a gonna die.
Sollozzo: I don't like violence, Tom. I'm a businessman; blood is a big expense.
Vito Corleone: I'm gonna make him an offer he can't refuse.
Answer: Luca wasn't Vito's bodyguard, Paulie Gatto was. In Mafioso circles the bodyguard is also usually the chauffeur which was the other part Paulie played. Luca was an independent who had loyalty to Vito. Unlike other members of the family, Luca had his own operation and his own scams. He was usually only called into service by the Don when some particularly nasty piece of business needed to be taken care of for which Luca was paid handsomely. Few people knew why Luca was loyal to Vito, it had to do with a bit of trouble Luca got into with a young girl, Luca was looking at some hard time and Vito was able to get him out of it. As explained in the books, Luca didn't care if he lived or died, he didn't even care if he was killed, but he cared very deeply that he wouldn't be killed by Vito. That was the hold Vito had on Luca which made his loyalty so deep. So far as the rest of the underworld was concerned Luca was just an independent contractor who worked for the Corleone's from time to time. If you'll recall when Kay sees Luca Michael tells her "he helps out my father sometimes." Barzini was probably the only other one who truly understood how deep Luca's loyalty went. So, why did Vito send Luca: Vito thought he was dealing with the Tataglias. Ten years prior to the Sollozo meeting there had been a Mafia war. Vito planned the strategy of the war while Sonny handled the tactics. The war was bloody and costly but the Corleone's were able to out maneuver the other families and come out on top. After that war Vito was top dog of all the 5 families. Had Vito been correct that Philip Tataglia was behind Sollozo, sending Luca would have been a smart move. As Vito mentions after the meeting of the commission "Tataglia is a pimp, he never could have out fought Santino." Tataglia would have seen getting Luca as a huge win, not only would he have Vito's special muscle, but he'd probably also believe he'd be able to get information from Luca. Where Vito made the mistake was not seeing Barzini pulling the strings, had he believed Barzini was involved he'd have handled it differently.
The line in Goodfellas seems illuminating here where Henry Hill explains that the Mafia is essentially an organisation that offers protection for those who can't turn to the legitimate law of regular society. This suggests that these "family" ties are not as strong as we imagine. These criminals are not a definite part of an orderly corporation, like head of HR at IBM, but a loose confederation of connections and loyalties that are rather more fluid. This is a theme also explored very well in the book and film, Donnie Brasco. Therefore, it wouldn't be totally unthinkable that someone in Luca Brasis position could turn to another "family" if he felt it expedient. However, these kind of guys have a tendency towards mistrust.