The problem I see with your complaint is that Skyrim had already been part of the Empire for nearly a millennium(?)
In this case, they were only with this empire coming into the Third era and currently the 4th. It doesn't help that They were basically shoehorned into the whole thing by the brilliance of Tiber Septim.
In all reality, the presence of the Imperial Legion was all the provinces needed to know they needed the Empire. The local Legions secured hostile locations and maintain the peace in each of the provinces, as well as providing relative security from just about every criminal enterprise in the Empire.
Hardly. The more prolific and, what may be considered to be socially harmful, guilds are still operating (to my knowledge) throughout the provinces. The legion is important to secure roadways and try to make travel generally safer, but I think 4E Tamriel, the legion is barely holding onto any threads to maintain order.
You can look at what happened in Markarth after the Imperial Legion in Skyrim was pulled off the region to fight off the Thalmor off the Imperial City.
True, but the city was reclaimed quite quickly after Ulfrics intervention.
There's propaganda on both sides of the war, some more extremist than others.
No argument on this front.
Despite Stormcloak propaganda and personal opinions, there are several times where it is included in Imperial dialogue that they are not comfortable with the treaty made with the Thalmor, but that it was necessary. There's a widespread agreement that the treaty was not fair, and that citizens of the Empire should worship Talos openly. Nobody is willing to speak up, because the Empire is not ready to fight another war.
The problem here is that they are soldiers, and their duty is to preserve the empire, regardless of their personal feelings. Some may not like the treaty just for the simple fact that they were bested, and not on the idea that Talos worship is being banned. The fact is, that Cyrodiil is more secular than it is sacred. Give it a good amount of time, and they probably will have not qualms with Talos being taken out of the divines, as long as there are those that continue to hit the subject over the head. Hell, Hammerfell seceded just based on the fact that the Thalmor was weak and they believed they could be taken out. True, the empire was reeling from the attempt to retake Whitegold, but if they really wanted to, its possible they could of pulled legions from the other provinces in a attempt to seal the deal.
Ulfric, our Thalmor agent buddy, on the other hand, decided to defy this decision that cost thousands of lives of Tamrielic races and try to destabilize Imperial rule by targeting a completely opposite problem (the Empire) than what is made apparent (the Thalmor), just so they can worship Talos. He also assumes he can take on the Thalmor all by himself while being equally scared of them (maybe even open up an alliance with Hammerfell, but this is also debatable).
He's totally not in it for the power, though and the murder of High King Torygg had no ulterior intent, even though Torygg was open to dialogue about the fate of Skyrim.
Ulfric is not a agent of the Thalmor, but people like to think that him as a asset to the Thalmor puts him in that line. His cooperation extended to the fact that the Thalmor tortured the man to gain info to take Whitegold. By the time he broke, the Thalmor already had it in their possession. I see no part in how he is scared of the Thalmor. By the time the Stormcloak questline is completed, they are committing all their resources into the forming of a professional army, rebuilding the rest of Skyrim in preperation of the Great War v.2. As for the murder of the High King, it was less of a murder (Although Ulfric probably knew he could kick his ass) and more of a old tradition of booting the guy you think is to incompetent to rule effectively. The High King under the Empire is more or less a title that has little bearing in the grand scheme of things, and his death sent a clear message to the empire what direction he wanted to take Skyrim.
Uflric is, quite frankly, absolutely not fit to lead Skyrim as a unified Kingdom; making the Stormcloaks' goals a complete farce made by a passionate, misguided politician.
I will not attempt to judge the man from that standpoint since we really have no clear cut of what his true intentions are. Ulfric just didn't fall off the bus and go military commando though, the man knows what hes doing, and to dangerous effect, especially at the end of the Stormcloak quest line.
If the Stormcloaks win the war, they would have to start all over. You have to understand most of these men were in it to overthrow the Empire's control in Skyrim and defend against the Thalmor, and nothing more. They are a militia with improvised weaponry and armor, and they are not very fit for conventional combat.
That is incorrect. Even before the end of the questline, the big thing Ulfric and his lieutenant stressed was kick the empire out, and rebuilding Skyrim in preparation of the Great War. Skyrim is wealthy enough to make it all happen on its own, while the Empire depends a good deal on her silver mines.
The Stormcloak army was struggling to combat a single completely local Legion, while the Aldmeri Dominion swept the rug off four entire Legions, wiping off two of them completely. The Thalmor are more than capable of completely obliterating Skyrim, assuming they have been building up for the next Great War
Going off of the history of the empire (And most great powers in Tamriel), it wouldn't be the first time a vastly outmatched army snatched victory from the [censored] of defeat, only to come and kick the opposing sides ass hard. Hell, Tiber Septim should be a testament to this.
If you want ingame proof, use console commands to pair off a couple Imperial soldiers against twice the number of Stormcloak soldiers or, if you're feeling adventurous, Justicars against Stormcloaks. You will see how unfit the Stormcloaks really are.
I have actually done this before, three Imperial troops against three Stormcloak troops, and in my case the Stormcloaks won out, all three imperials dead, and not a single Stormcloak slain. I can't say I have tried a Justicar though. Problem is that powerful mages in game will kick the crud of just about any warrior NPC, and I can't take it as proof of their superiority. Keep in mind that the Aldmeri dominion makes heavy use of Bosmer, Goblins, and potentially Kajit in their armies.