But wasn't the Dragon Reborn always there at the end of an Age? They lost that knowledge?

There was always a Champion of the Light born, yes, at the end of an Age to fight the Dark One, however the term "Dragon" is a recent (or reused, considering we're talking about cyclical time here) appellation.

As for losing the knowledge of a Champion taht fights at the end of an Age, I don't see why it couldn't happen. Really, the only reason LTT is remembered is because he is directly tied to the Breaking and all the suffering that came after (the loss of paradise). I don't see why a world-hinging battle couldn't happen quietly in a way that only those directly involved knew what was happening.

So, that's about 516 ft (12ft per floor)? To put that in perspective, the Eiffel Tower is 1,063 ft.

If Moiraine was channeling on her own before she went to the Tower, why was she never referred to as a wilder by the other Aes Sedai? It seems like something that should have come up at least in NS when she and Siuan learn about the AS hierarchy, which places wilders a little lower than their actual strength in the Power. Yet Moiraine was never called a wilder or given any indication in her thoughts that it was something she'd kept secret from the other Aes Sedai.

I believe the connotation of "Wilder" is not a definition of someone who channles before becoming Aes Sedai, but rather a definition of someone who has channeled long enough to train themselves how to channel the OP without killing themselves. Basically, a "Wilder" is of the level of Accepted (if not full Aes Sedai in potential and skill), which is why Nyneve was raised to Accepted right away. I don't recall anyone thinking it was particularly odd that this was done with her, which leads me to believe that it had been done in the past with other "Wilders."