The timeframe between episodes is unclear, but a few references imply that most of the Gaang's adventures from the cartoon are happening offscreen in at least some form.
The fact that Roku, Kyoshi, and Kuruk all insist that an Avatar must work alone makes sense for their lives specifically, even though by all indications every previous Avatar has had companions like Aang. Roku was betrayed by a friend in his final moments, Kyoshi outlived everyone she ever loved, and Kuruk hid his pain from his friends because he was the only human who could enter the the Spirit World and carry out his duties, which led to his early death. They all have understandable reasons to be bitter on the topic of working with others.
Pakku agrees to let the women waterbenders join the fight, but initially his orders are to merely repair the walls—that is, healing damage. Baby steps.
Zhao refusing to kill the Ocean Spirit was likely Pragmatic Villainy. Legends say that the waterbenders owe their lives to the Ocean Spirit, but what does that mean? Will every waterbender drop dead if it's killed? Every member of the Water Tribes? Or even every single human? Zhao doesn't know, so he goes with the comparatively simpler solution: Eliminate waterbending itself, which the Fire Nation doesn't need and has only ever been a problem for them.
Fire Nation strategy:
The Fire Nation makes incomprehensible military choices, e.g. sacrificing the 41st Division to attack an already surrounded army of Earth Benders, losing an Armada at the North Pole to somehow distract everyone from the Fire Nation attacking Omashu. This isn't because the Fire Nation military brass are cunning strategists. It's in fact the opposite: they're actually really bad at military strategy. That's why the Fire Nation still hasn't won the war after 100 years!.
More specifically, they're led by Ozai, a Social Darwinist who makes his subordinates compete for his approval, writes off casualties as the weak getting get what they deserve, and does not accept criticism from anyone. This is the kind of dysfunctional leadership which makes it hard to keep occupied areas under control, let alone conquer new territory. Without a massive boost from something like Sozin's comet, the only major advantages they have are propaganda and indoctrination (which is probably why all of their soldiers have not deserted yet) and their technology (and even on that front, they have to steal designs from the Mechanist). Sozin himself admits that without the comet the Fire Nation would have been beaten by the Air Nomads, a society of Martial Pacifists who don't even have an official military.
When Aang asks Iroh whether the latter believes in the imperialist ideology of the Fire Nation, Iroh does not answer the question and instead talks about sending Aang some "soothing" jasmine tea. In a way, though, that is his answer: Iroh no longer believes in conquest, but would rather live in peace drinking his tea, and he wishes the same for those that the Fire Nation has deemed to be their inferiors and enemies.
In the last episode, the Moon Spirit is killed, and all waterbenders lose their power. However, Yue freezes Sokka's feet so he can't stop her from performing her Heroic Sacrifice. How does she still have waterbending? Because she's the last remnant of the Moon Spirit. It's even possible that realizing this is what led her to realize she could take its place.
As stated by Iroh in the original series, lightning is precise and deadly. These are characteristics that would be appreciated in an archer.
Unlike most firebenders who shoot fire with an open palm or closed fist, Azula uses two fingers with a motion that mimics firing a gun. Bows are the closest thing to guns in this setting.
Two of Azula's companions are Badass Normals, so she already sees value in non-bending skills. Mai and Ty Lee's particular specialties are also similar to archery: Mai fights with shuriken and throwing knives while Ty Lee is an expert in chi blocking, a martial art that targets specific pressure points to neutralize the enemy. This also ties into Azula being the one the loan out the Yuyan Archers to Zhao in this adaptation.
Zuko also specializes in a form of nonbending combat, except his is swordfighting which requires fighting up close. Archery is a ranged art that requires more strategy (examining angles, distance, probability etc). The two siblings are further characterized and contrasted through their preferred weapon.
Zuko's crew being the Fire Nation soldiers he spoke out in defense for in this show adds another layer to his harsh attitude towards them. Showing compassion for these particular men is what got him banished in the first place and they serve as a reminder that his father views him as a disgrace.
Zuko's scar is less in this adaptation compared to his animated version makes more sense as this Zuko (reluctantly) gives a decent fight to Ozai. His father burned him less because he assumed that Ursa's influence wasn't as strong on Zuko and, in a twisted way, "rewarded" him with a lesser punishment for not following his Social Darwinist path.
It could be a case of Call a Smeerp a "Rabbit", with Division meaning something different within the Fire Nation.
Even in real life, the definition of a military "Division" can vary depending on which military you're talking about; there's a lot of difference between having 6000 soldiers and having 25000 soldiers.
Gyatso's exposition of Koh has him voicing over a scene of the Face Stealer draining one of his captured victims into a husk, which he claims destroys their soul forever. It's never made clear whether this is just a generalized portrayal of his feeding or whether he was actually doing this at that instant to some of the villagers he had previously captured...
