I care not about how the entire FN royal family was portrayed; in fact, I even say that was one of the adaptation's few improvements over the original, but why on all things sacred did they make Aang skip waterbending in season 1?
They should've been more extreme with how Aang masters all bending arts. I imagine that Aang not only masters all bending arts and all possible sub-bending techniques, but he also fully adapts to all nations and their societies, being able to adapt to the norms, morals, rules, laws, crimes, politics, economics, business, religions, skills, etiquette, cultures, ethics, etc. of all nations, and essentially becoming a one-man team avatar.
This could be reflected in how Aang dresses. You know how Katara and Zuko have a painted and a blue spirit, respectively? Well, instead of Aang having one alter ego, he can have three. Each embodies both positive and negative aspects of all the other three nations and elements.
In season 1. Sometime after he finds out about the fate of his nation, he accidentally kills an FN soldier. This naturally traumatizes him, and Katara comforts him. Sokka tells Aang that if he wants to live and protect others, he'll have to take some lives as well. Aang is taught how to hunt and gather food the way the water tribe does it, and, to his reluctance, Aang starts eating meat. Katara also had the waterbending scroll for her entire life, Gran-gran was training her in secret, and was already a semi master by the time she met Aang. Katara teaches Aang everything she knows. His hair grows out sooner. Hama is introduced sooner, and through her, both Aang and Katara learn bloodbending. Right before making it to the North Pole, Aang dresses up in that water tribe warrior outfit Sokka had on in the animated pilot, and Aang even wears the same war face paint. While Katara tries to prove herself to be a fighter to Pakku, Aang wanted to look into waterbending healing. Eventually, Aang learns bending healing as well.
In season 2. Aang's hair is longer, and he puts on an outfit that's a mixture of a Dai Li and a Kyoshi Warrior. Aang is colder and harder than ever and has gotten a little better at killing. In the desert, after Appa's been taken, Aang goes ballistic at Toph, but Toph fires back at him, saying some boundary-pushing insults. This causes Aang to lose it and severely beat down Toph. Sokka and Katara pull him off, but he hits them really hard as well. Overcome with guilt, he leaves the team behind. He finds the sandbenders who took Appa before the gaang finds him. Without Katara to calm him down, Aang goes into the avatar state and brutally massacres and dismembers all sandbenders. He has a mental breakdown after witnessing the carnage he has wrought. The gaang finally finds Aang, but he barely utters a word, like he's just an empty shell now. It's the season that both Aang and Toph achieve metalbending, but Aang manages to achieve lavabending. Season 2 ends with Zuko and Azula successfully capturing Aang and forcing the gaang to reluctantly leave without him after Katara saved him from a lightning strike.
In season 3. His hair is even longer, and he spends all of season 3 only wearing his headband and Kuzon persona outfit. Aang has been assigned to be Azula's personal prisoner; wherever she goes, he goes. Whatever order he gives him, he must obey. Azula uses Aang to kill off FN traitors, causing pollution and famine in an FN village. Aang does so without question, barely having any life left in him anymore, but not before Aang is taught how to kill with firebending. Aang is with the core fire four at the Ember Island beach. Parts of Aang's old self started coming back to life. Aang and Azula dance together, and he sympathizes with Azula about her somber view of herself as a monster. He relates to her, big time. After that, Aang and Azula act warm, friendly, lively, and even happy toward each other. They are invited to a war meeting. After the plans to destroy the Earth Kingdom have been made, Aang and Azula have a heated falling out. She orders Aang to be transferred to the boiling rock, but Azula feels more guilty and conflicted than before. After the day of the black sun, after Zuko fully decides to join the other team, Zuko brings Aang with him and hands him over to the gaang, in exchange for letting him join. Aang and Azula miss each other and secretly dread the possibility of them being enemies again. Aang even saves her from falling at one of the air temples. In the debate over Ozai's fate, Aang wants Ozai to live mostly for the sake of Azula.
In season 4. The war hasn't ended yet, Ozai hasn't been usurped yet, and the comet won't arrive until the finale of season 4. But the final agni kai between Zuko, Azula, and Katara happened at the finale of season 3. Azula's mental disorders are worse, worse to the point where she can't even lightningbend, due to Aang being gone. Instead, Zuko takes a regular fireball for Katara. In this season, Aang regains his air nomad roots. He meets Guru Pathik and has him relearn all airbending lessons, while also teaching him about chakras and potential flaws in the air nation. Aang finally shaves his head and starts wearing air nomad attire again. The redemption arc for Azula gets executed here and is done almost like what Aaron Ehasz had in mind. But the difference is that Aang helps her reform too, and they both even begin to fall for each other. Aang and Azula go to a remote island, and they open their chakras together. It rains after their last chakras were opened, and Aang achieves all possible airbending techniques. Not only did Aang become a fully realized master avatar, but he became a one-man team avatar. Azula, Mai, and Ty Lee make up and join Team Avatar permanently. After the war is done and Zuko is the next fire lord, Aang has an outfit that represents each nation, and the entire team looks out at the sunset together.
"It is important to draw wisdom from many different places. If you draw it from one place, it becomes rigid and stale. But understanding others, the other nations, and the other elements, will help you become whole." Aang, of all people, should understand this better than anyone.