I've literally only just watched through all of The Last Airbender and Korra for the first time- and a few issues to address here
Firstly- to address Brian's issue with the term airplanes- I only ever caught them being referred to as Aircraft, which is a much more readily extrapolated term for a first time encounter with such craft... It is possible I missed the reference to planes, so if you can provide a time reference, I'm more than willing to accept your point on this one.
Secondly- on the matter of Korra knowing she was the avatar before being told, from what I understand of the lore of the series, the avatar is the only personn of their generation to have more than one type of bending- and thus the evidence was irrefutable by the time that the White Lotus Guards turned up (after all, its not as if there were any other candidates who could prove any skill in two or more forms of bending to provide any contention in the matter).
Thirdly- on the loss of forms in bending. I see this as a reflection on the march of time and supposed progress in the intervening seventy years, which take us from something akin to the beginning of the industrial revolution during the time of Aang to an analogue of early twentieth century New York (with an Eiffel Tower analogue for good measure) in the time of Korra. As the renaissance and the industrial revolution here on earth made the traditions that came before seem irrelevant, I imagine something similar happened around Republic City over the intervening seventy years- with many people trying to change with thetimes rather than sticking to the seemingly archaic forms and spirituality of the past.
All that being said, the main issue that I had coming to both Avatar and Korra from an anime watching background is that the series were too short for my liking, with the effect of forcing both series (Korra in particular) into a breakneck pace that allowed next to no time for character development and the slow buildup of foreshadowing and exposition that might have given hints towards the sudden reveals concerning Tarlac and Amaan, leaving Korra as a series that blurred from one moment to the next as it tried to wrap itself up within a paltry twelve episodes, losing out on pacing and coherence in the process.