Did Aang continue fucking Katara and Toph? I was under the impression that only MC fucked them in Aang’s body. That’s partly why Katara is able to immediately recognize MC in part 3 and 4; Aang just carried on with how he would normally behave in the show and only started behaving differently in Ba Sing Se when MC possessed him again. Actually I forget what happened in Part 2. Did MC ever reveal he was inhabiting Zuko/OC at the end? I’m pretty sure Toph found out the real situation because Katara told her who was really fucking her.
Aang behaves like he would in the show when the MC isn't inhabiting his body i.e no fucking Katara or Toph. The reason Katara recognized the MC in Aang's body is still unclear, she also saw the MC's spirit floating out of his body in Book 1, which is also unexplained, plus she seems to know what the end goal of the MC's journey is before we do, which is why she even helps the MC seduce Toph.
In Book 2 the MC does regain his memories by the end and tells Azula and Mai that he's going to lose his memory but he promises to come back, which I don't know how that's going to happen now that the MC has jumped decades into the future and mastering Airbending is the last thing he needs to do to complete his training, after which there shouldn't be a reason for the Spirit to take him anywhere except present time.
Katara did explain the situation to Toph, along with whatever else she knew, because even Toph seems less angry and more annoyed when we meet her in Book 4, and if I remember correctly says something along the lines of not telling the MC what she knows to get back at him for impregnating her and leaving without an explanation at the end of Book 3