So, you can tell me why Aang became a giant spirit fish at the end of Water?
Wasn't an ordinary AS activation. The ocean spirit took hold of him and used him as a medium to destory the fire nation for revenge.
Or why Avatars can physically manifest themselves?
I don't think it's an actual manifestation so much as it is visual projection. It's established that spiritual entities can project visions, not just in terms of the AS, but in various aspects. Aang, Sokka and Katara got various visions in the swamp for example. Otherwise, spirits can manifest themselves for real, like the panda spirit in that one episode. So the rules are pretty consistant here. A better question would be why wouldn't they be able to manifest themselves?
Or maybe why Azula just has blue fire?
Because people who are really damn good at firebending can produce unique flames. This isn't just blue, but various colors, as shown in The Sun Warriors. What does this even have to do with the Aang's AS though? The blue fire was mostly a narrative indicator of how Azula was special, but she could have had normal colored fire and just been a normal but really awesome firebender and the show would remain the same. Understanding how the AS functions on the other hand is a critical piece of plot so that we know what the heroes can and can't do to beat the villain. It's not really comparable to just knowing some trivia information on Azula's abilities.
Honestly, it looks more like you just haven't been paying attention to the show. There are reasons given for things happening pretty often.
Her getting her AS isn't that vague at all. She was at her lowest. Let's say that that whole bit was about spirituality, and not necessarily duress. People have been known to become spiritual in their most dire moments. I don't really think that Air's ending requires that many jumps in logic. We learn in ATLA that healing using waterbending involves chi paths. We know that chi points can be physically harmed, and we also know that chi controls bending. It's pretty clear that Amon physically seals chi points within the body using bloodbending, and it honestly makes sense. At least to me.
They establish that healing uses chi paths in one particular technique, and later with lightning bending. I don't think that is a go ahead to assume all bending is fundamentally based on chi paths, or that this is what Amon does. Second, one can become spiritual due to a dire event depending how you react to it, but it is not inherent to the dire event itself. Bad shit happening to you and feeling sad doesn't automatically make you spiritual, it's in how you deal with it.
Guru Pathik may have given Aang a way to control the Avatar State, but the good Guru also said that if Aang left before opening the final chakra (which are big ol' pools of chi) that it would be sealed forever even though he was able to reopen it awhile later in Ba Sing Se. Then it got zapped by lightning, which sealed it, and reopened with a rock just because...why? I mean, Katara apparently couldn't heal it, even though she could sense that there was a blockage of chi there. When she tried to heal it, he suffered a flashback to getting hit with lightning. Just like Korra's PTSD in Balance. Yet somehow, getting hit with a rock unblocks all of the chi, gets him over his PTSD (after cowering in a rock for awhile), and then he can immediately control it at will.
No, what he said was that if he left before he was finished, he would be unable to use the avatar state until he completed the last step that they never finished. Aang did that in the season 2 finale.
As for the lightning and rock, chi paths are evidentally affected by physical things. Katara couldn't heal Aang because once she tried to apply pressure, he squirmed away in pain, so she stopped. One possible difference is that the rock applied the pressure whether Aang wanted it to or not. Also, Aang was not suffering from PTSD in the remotest sense of the word. It should also be noted that the activation of AS wasn't a proper one at first, during Ozai's fight. Even though the chakra point was 'released' by the rock, Aang was in his glowy, monster version of AS, when the proper AS is the one he did at the very end where his eyes only glowed for a second, wherein he was in complete control over his actions. If the chakra pool was free in the way it was supposed to be, that wouldn't have happened.
While I do agree that Korra's being able to enter the AS at will does come a bit fast, considering she was far more eager to attain her full Avatar abilities as opposed to Aang, it would make sense that she was able to come in to it much quicker. Even then, she couldn't totally communicate with her past lives in full. If I recall, she struggled with that quite a bit, which is why she was so quick to jump on the "Unalaq is da best" bandwagon.
No, because she doesn't complete any of the steps on how to activate the AS that were establlshed in the Guru episode, and they don't really establish any idea that there is an alternative way. She can want to be the best avatar evar as much as she wants, but that should not happen if she is not shown doing the things necessary to make it happen. If Korra wanted to study physics as much as she wanted to be the avatar, but she never opened a physics book or done experiments or made any efforts to correctly understand physics, but then somehow displayed an accurate knowledge of the subject, that would be bullshit. We see Korra incorrectly doing spirituality all season, but she gets it right at the end even though the events that occur within it go against established rules of how things work because she wants them to? How is that not awful storytelling?
