Sal Marcano attempting to give Lincoln Delray Hollow seems like a strange gesture given he's been back just a few days. Except, Sammy has been screwing up business for quite some time and his heir apparent is an Inadequate Inheritor. Sal probably realizes his back-up plan of the Dixie Mafia isn't a good one and wants a smooth transition to someone trustworthy. The fact Lincoln refuses the offer forces his hand.
Of course, given Sal betrays both Burke and Vito out of their shares as well, it's very likely that he was always intending to take their cuts of the heist. You Have Outlived Your Usefulness seems to be a common habit of Sal Marcano. Attempting to persuade Lincoln get rid of Sammy and Ellis would just make sure the Black Mob was in no position to retaliate.
Lincoln is a Shell-Shocked Veteran and career criminal who easily overwhelms the less talented The Mafia with his superior grasp of violence as well as psychological warfare. The public reacts in both shock and horror at his actions but he achieves his ends despite this. The developers have successfully justified your typical ultra-violent video game protagonist's rise to power!
Several of the Marcano mob refer to Vito as a "carpet bagger", a Southerner term for businessmen from the North taking away money or jobs. This shows how much the local Italian mob have gone native and forgotten their roots.
It is also possible the Southern Union is Hiding In Plain Sight given the Ku Klux Klan had numerous periods where it was assaulted by the government for, well, being domestic terrorists and a hate group despite widespread support from racist whites. Real-life organizations which are the Klan in all but name (or consider themselves such in private) operate under new names and affiliations.
Lincoln actually outright confirms that the Southern Union is not a Captain Ersatz in conversation with Donovan. He describes the Union as being a branch of the Klan.
Something else that may seem odd at first glance in terms of gameplay but makes sense narratively. When you take on one of the two underbosses in a neighbourhood, the mission you are given is to confront them, the exception is Chester Moreau who heads up the Southern Union.
Father James choosing to kill Lincoln Clay with a car bomb seems like it comes out of left-field but the circumstances which trigger it make sense. Father James is disappointed beyond measure if Lincoln chooses to become The Don and rule over New Bordeaux with his lieutenants but he accepts it. However, if Lincoln kills his lieutenants then he's doing exactly what Sal Marcano did and shows himself to be worse as he does it without even a living family to justify it. It also makes sense Father James would know how to do this given he was a mechanic during WW2.
The game's plot is one of Dramatic Irony when you finally find out all of it. Sal Marcano is sick of being a mobster and wants to protect his son from danger by going legitimate, so he betrays the Black Mob and makes an enemy of Lincoln Clay who dismantles his empire before killing his son, then potentially him. Sal's previous position in the city was secure with the Commission happy with him, the Black Mob subdued, the Irish Mob willing to work with him, and the Haitians dealt with by Lincoln. Even the public respected and liked him. It was Sal's desire to go straight which destroyed him.
Sal Marcano has Olivia Marcano murdered when she's defeated. This is despite the fact Olivia is loyal and still a massive source of income. However, she murdered Sal's brother and if his nightmares comment is anything to go by, this was a Best Served Cold scenario. With his casino almost ready, Sal no longer needed her or her society contacts.
Doucet's Blatant Lies to Lincoln is because he probably can't tell black people apart due to his racist views, so he can try claiming he wasn't there since there was no witness left in his head.
Alternatively: Giorgi shot Lincoln first before the massacre began, and from Doucet's side it must have seemed Lincoln was unconscious when he stabbed Ellis, so he believed he had plausible deniability.
Lincoln's lieutenants are Haitian, Italian and Irish. All three groups have at one point or another faced discrimination in America thanks to either Nativism, white fear or both.
Sammy is a character we get to know only briefly but everything about him suggests he is a Affably EvilFriendly Neighborhood Gangster at worst. He even regrets sending Lincoln to kill Baka, despite the fact the Haitians are threatening both his family as well as livelihood. How would he feel about the fact Lincoln is murdering potentially hundreds of people to get revenge for him?
Frank Pagani seems confused as much as terrified when Lincoln finally tracks him down (and runs him off the road before finishing him). He even says, "I haven't done anything to you." Lincoln doesn't explain and interrogates him before letting him die. Unlike Richie Doucet, who denied a part in the Black Mob Massacre, Frank actually couldn't have been involved because he's been in Cuba the entire time Lincoln's rampage was occurring. Frank genuinely doesn't know who Lincoln is or why he's murdered all of his men before killing him.
The revenge plot. Sal commits suicide after you murder his son and it's also made clear he's hated being a mobster for almost the entire time he's been involved with it. He expresses no real regret over the loss of his empire as he had been planning to go straight. In effect, Lincoln's entire war against the New Bordeaux underworld was pointless. He could have just killed Giorgi and achieved the exact same devastating result on Sal's psyche.
This adds a bit more brilliance and horror. Lincoln doesn't just want vengeance or street justice, he wanted to make Sal feel the same way he felt. Father James, however, warned him that the path only lead to darkness and corruption and the game shows that. Lincoln could easily have killed Giorgi first since he definitely knew how much he mattered to Sal, which would have hurt him, and then take out the Dixie mob to free the city. But Lincoln's quest was actually one of conquest through the game, and makes James' argument for leaving the city sensible. If Lincoln stays, he's also worse than Marcano in many ways since Sal was attempting to go straight.
Although it should be noted that Giorgi was never on Lincoln's list, while he had no problem killing him Lincoln still didn't plan a revenge scheme on on his old friend and had Giorgi skipped town, Lincoln probably wouldn't have killed him.
If Lincoln accepts the Commission's offer to let him run New Bordeaux in exchange for a cut of the profits, he actually ends up in Sammy's exact same position before the Federal Reserve Heist. He's the head of the Black Mob kicking up a bunch of money upstairs to White Italian gangsters. The only difference is the size of his territory.
When Lincoln turns down Sal Marcano's request to take over Delray Hollow, he finally decides to get rid of the Black Mob. But considering Sal's real plans, things probably wouldn't have gone Lincoln's way even if he did take Sal's offer: Sal Marcano soon reveals that he wants to work independent of the mafia and the Commission, which includes abandoning much of his criminal empire in order to go legit. Even if Sal avoided mistreating Lincoln as the new boss of Delray Hollow, he'd still be leaving him behind with the rest of his underlings in New Bordeaux once his casino plans succeeded.
"Most of the cops in this town are in Sal's pocket. They see you fighting Sal's goons, they're coming after you." As this guy points out, if Marcano controls the police to that extent, it seems strange that they were such an issue during the Federal Reserve robbery, especially since that Marcano's son was helping rob the place.
The answer is in the name: Federal. Employees of the federal government are harder to bribe than dirty cops who are more interested in keeping the racial status-quo. Furthermore, there is a limit to what cops on the take will tolerate. Becoming accessory to counterfeiting is not something they won't do, because that brings the FBI to town. And the South really hated the feds coming down to their states to poke around and go carpetbagging.