What if the heart wasn't destroyed yet, I know it's game mechanics, but if the heart was still there would she still be killed by flame sword?
My guess is Bethesda just assumed players would finish the Morrowind main quest before doing Tribunal, and it was probably just an oversight that you could do it before then, in any case, it certainly makes most sense if you wait until after finishing the Morrowind main quest to do it. In fact, it probably makes most sense if you didn't even install it until after finishing the main quest, or at least until after attaining a certain level of progress in the original game, due to the Dark Brotherhood attacks not much reason to send assassins after some prisoner who just got off the boat.
In any case, I think it's safe to say Almalexia is dead, but even after people learn about that, I'd imagine that the Temple would still revere her and the rest of the Tribunal as saints, just as they do for Nerevar and Veloth.
Vivec was rumored to be taken by the daedra wasn't he? Seems to me like the devs way of getting him out of the way, leaving the player to decide whether he has disappeared, or has been killed by the nerevarine.
That's probably the case, my guess is that it's a similar thing with the rumors that the Nerevarine went to Akavir, they wanted to take him out of the picture somehow, but leave room for players to decide for themselves what really happened.