Much as I love Tarantino's movies, I've never found them to have nearly as many strong racial messages as he usually claims they do. As you've pointed out, some of the scenes he writes are actually problematic from a racial perspective. However, I do think this movie has some things to say about race, it's just maybe not what we'd expect.
The theme of The Hateful Eight is hatred—it's right there in the title. Most of the plot is motivated by the characters' hatred, and most of the hatred comes from the Civil War. The war had strong racial underpinnings, so the hatred also has strong racial underpinnings.
Major Warren seems to hate whites; he says a couple times in the movie that he fought in the war and later became a bounty hunter just to kill white people, and he shrugs off the deaths of the white Union soldiers when he set fire to the camp where he was imprisoned. His hatred is reinforced by the stream of bounty hunters that came after him in search of the money on his head. Because of his life as a slave and his experiences during and after the war, he mistrusts all white people to the point that he made a fake letter from Abraham Lincoln to show to whites so they would warm up to him.
Possibly, this is what Tarantino meant when he said in the interview that the movie was about "white supremacism". The post-Civil War society is still unequal with regards to race. That inequality breeds the kind of mistrust that we see from Warren. Warren knows that, even if he's a free man, there are a lot of white people who won't respond well to him as a black man. Since the whites still have so much power in society, Warren has to deal with them on a personal level, no matter how much he mistrusts them. He manipulates them using the fake Lincoln letter because it links him to someone these white people respect, and makes him appear respectable by association.
Chris Mannix and General Smithers both hate blacks, though the two men's hatred has a slightly different character. Smithers seems to genuinely, at a personal level, hold black people in contempt as less than human. Since he was a slave owner, it makes sense that he would develop this attitude. Interestingly, he does seem to warm up a bit to Warren when Warren makes overtures of respect, just before he provokes Smithers with the story about killing Smithers's son. I get the impression that, in addition to being racist, Smithers is an "aristocrat" who, since the war, hasn't been getting the respect he feels he deserves. Back when he was a general, he probably would have regarded someone like Mannix as beneath him as well, but he's become so desperate to be respected that he's even willing to take it from low-class people like Mannix and Warren.
Mannix is a lost-causer; he's enamored by a vision of the glory of the South. He blames the former slaves for destroying the glorious old South, lacking the imagination and compassion to understand why they would do such a thing. He was never actually a part of this glorious old South; from what I remember, he implies in the stagecoach that he was quite young when the war started, and that most of what he knows about the old days comes from his father. He didn't own slaves and he didn't make his living off their labor, but he hates blacks because he was taught to, and hasn't got the brains to question those teachings.
There's mutual personal hatred between Warren and Smithers, on Warren's part because Smithers summarily executed his black captives at the Battle of Baton Rouge, and on Smithers's part because he can't stand the nerve of a black man becoming a cavalry officer and fighting against him. Warren ends up killing Smithers, because he can't get over his personal hatred for him.
On the other hand, there isn't any personal hatred between Mannix and Warren. Mannix is a racist, but his hatred for black people, is distant and weak enough that he can overcome it when it's to his advantage. And Warren was clearly willing to work with white people if it suited him. Maybe he can never really trust them, but he'll work with them, and he'll keep one eye on them in case they show signs of turning. That's why, when it's to their mutual advantage, Warren and Mannix are able to team up. It's not a great moment of racial unity. It's purely selfish.
For me, that sums up the first and third scenes mentioned in the OP. Warren and Mannix's alliance was not about race at all. Mannix doesn't seem to take Warren's race, or even the fact that he killed Smithers, into consideration when he chooses who to side with. He chooses the side that gives him the greatest advantage. Maybe he also cared, just a little, about the law that he would have enforced as the new sheriff (assuming he was telling the truth. I tend to believe he was), and couldn't bring himself to side with the outlaws. I suppose the message you could read from this is that two races who hate each other can team up out of self-interest, and maybe learn to tolerate each other. It did seem in the final scene that Warren had some respect for John Ruth, so maybe we're meant to understand that he learned to trust whites a little more; and Mannix seemed, over the course of the movie, to step back a little on his racism, culminating with his decision to team up with Warren against the outlaws.
Smithers and Warren's mutual hatred was personal, not purely racial. It was amplified by race, at least on Smithers's part. But he went for the gun because he hated Warren personally, especially after Warren goaded him, and Warren set the situation up because he hated Smithers personally.
I think your reading of the second scene is correct: the gang members would have killed whoever was there, regardless of race. They leave Smithers alive because he's old and apparently harmless, and because they think he can help their cover. Not much of a racial message here, although we do see that Minnie and Sweet Dave are an interracial couple, which would have been exceedingly rare in this time period.
As for the fourth scene, this bothered me when I saw the movie, and I consider it a plot hole. Warren claims that Minnie used to have a sign saying "No Mexicans or dogs" that she took down when she started allowing dogs. But we don't see any evidence that she hates Mexicans when the outlaw gang's stagecoach arrives. She seems to receive "Bob" just as warmly as the rest. There are various ways you could explain this, but the movie doesn't bother to.
In the end, I don't think the movie conveys a single clear message about race. It uses race and racial hatred as a fundamental part of its plot and characterization, but it doesn't seem to have a single big message the way, say, American History X does.
