Rule of Symbolism: Throughout the film, Irulan's clothing gets closer and closer to looking like a standard Bene Gesserit. Additionally, she starts off the climax by wearing a "cage" over her mouth, opens it up before Paul's little chat, and speaks up to save her father, in a way certainly not really planned by the BG, the Emperor, or maybe even herself.
In the first film, Baron Harkonnen ordered his men to leave Jessica and Paul for dead in the desert. When Paul kills Harkonnen, Paul tells the Fremen to leave the body for the desert. If the stabbing didn't kill Harkonnen, the desert sure did. Plus, puppetmaster Harkonnen dies on the steps of the throne he coveted, unable to get to it because his own "strings" have been cut.
The movie sets up a more plausible explanation for the Fremen's takeover: Paul is the official heir of House Atreides, the de-facto ruler of House Corrino via marriage, and the last surviving leader of House Harkonnen — a potent combination of major political capital that essentially legitimizes the Fremen's war. For context, the jihad is the equivalent of the US, Russia, Europe, and China uniting to conquer the world.
The Harkonnen society seems to revere their leaders as sacred and almost divine, so when Paul declares that they will win by "being Harkonnens", he is embracing his own cult of worship.
In the prior film, Shaddam's portrayal was criticized for being out of character — he made no effort to hide the Sardaukar's involvement in the attack and risked igniting a civil war (especially egregious given Mohiam had explicitly warned the Baron that the Sardaukar's participation could never be known). With Part Two's reveal that Mohiam was the conspiracy's true architect, that seeming arrogance gains new meaning.
While it's not explicitly stated, it seems plausible that the Bene Gesserit wanted the Sardaukar's involvement exposed; they were setting up Shaddam to take the fall with the Landsraad if/when things went south.
To further speculate, perhaps they needed Shaddam out of the way if they were to elevate the Kwisatz Haderach (who was at least one more genetic generation away from manifesting at the time of the plan's conception).
Stilgar's "The Mahdi is too humble to say he is the Mahdi" is funny, and the Monty Python's Life of Brian similarity is noticed. But there is something to this, both stories are about the absurdities of religion, or placing too much faith in a single person. Brian's followers did get out of control some times as well, such as attacking the old man out in the desert.
Frank Herbert came up with the name "Harkonnen" based on the Finnish surname "Härkönen", which he found in a local phone book while looking for a name for the antagonists in his book. While Herbert probably didn't mean it so, one could speculate that the Harkonnens in Dune did in fact descend from a Finnish family named Härkönen, with their surname mutating into Harkonnen at some point. If that's the case, it's fitting that Feyd-Rautha is played by Austin Butler, who himself has some Finnish ancestry on his mother's side.
Leto's plan when arriving on Arrakis is to cultivate "desert power" by working with the fremen, building up his house's power again after being removed from their original planet. Paul, in a roundabout way, does exactly this: Gets the fremen as his allies and soldiers, builds a "desert power" army, and under the atreides banner they take control of Arrakis. It's just done in a far more destructive way for the emperor and a lot of other people in the known universe.
In the film, the Fremen are broadly divided into two groups: the southern and northern tribes, with the southern Fremen being more fundamentalist and the northern Fremen being more nationalistic. Paul, wary of the prophesied jihad, initially refuses to go south in an attempt to circumvent the propecy. But later on, Feyd-Rautha's carpet bombing of all the northern sietches thinned out the northerners in Paul's army, which allows Paul's (now majority fundamentalist) army to lead the Fremen into a galactic holy war. The question is...did Paul plan on sacrificing the northerners as cynical political maneuvering? Or is this the prophecy overwriting Paul's attempts to avoid bloodshed?
When advising Chani to keep her head down, Gurney alludes to how Rabban killed his family years ago, confirming that his original backstory from the book has not been changed or Adapted Out. Despite this, when confronting Rabban in the climax Gurney makes no mention of his first tragedy, and he instead adamantly states that Rabban's death is "for [his] Duke, and [his] friends". Gurney may not be Fremen himself, but he's just as radicalised by his loyalty to Paul and the Atreides as they are.
