I don't recall Egwene ever claiming to be the Dragon Reborn or that she was fated to fight the Dark One or win Tarmon Gaidon. In Book I, she fought to defend him against the Forsaken buying him time, she worked with him in the Aiel Wastes and her POVs after uniting the Tower showed that she recognized he was the Dragon Reborn while being concerned for his sanity based upon reports.

So your prediction on the first point was wrong and based on faulty assumptions (and mistaken inferences which beg the question you were insinuating).