2) It never explicitly reveals how she did, although the hunters that Egwene assigns to finding Mesaana (the former black ajah hunters) come up with three ways it couuld be done. She could have been holding another oath rod (obviously with an inverted weave hiding it) that unbound her when she swore. The second possibility is she may have put someone under heavy compulsion and a mask of mirrors and sent them to swear in her place. The third and most likely possibility is that they discover a weave that can make people hear something other than what you say. For example, you could say "I swear I'll lie whenever I feel like it" and everyone hears it as "I swear to speak no word that is not true." This weave can be inverted and tied off so they wouldn't detect it.