1) Not 100% sure on this, but leaning toward the revelation that Mat's Ashandarai is the key to exiting Finnland

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.

3) Nope, but lots of other people do.

4) She can channel, but is much weaker since the Eelfinn drained much of her power. She no longer is strong enough to have attained the shawl. However, Moiraine has that Angreal that lanfear had been using whcih makes her more powerful than she was before.

5)Aran'gar, Delana, Asunawa, Jaret Byar, Katerine, Mesaana (basically), Nicola, Carlinya, Shevan, Noal (Jain Farstrider)