She had to make the questions touching on the Shadow about herself, that seems to be the key. We don't know exactly how the Finns do it, but it's very clear they can answer any "serious" question related to the future (and possibly past) of the person in front of them (I wouldn't try to ask them if you should eat chicken or beef next monday...). It's extremely similar to what the ter'angreal in Rhuidean does, with some major differences: the rings throw at you a ton if not all the "nexus" in your future, with all their if/then branchings and variations. I believe it gets this information by "scanning" the Worlds of if where all that's possible happens. The human mind can't process all that information. Most but a few memories from the scanning get wipe out from your conscious memory very fast, your inconscious absorb more that return as "hunches" later and so on. The Finns visited while in Tear seem able to scan through all that information and find what's related to your questions. Their answers aren't very clear. It may be because of the variations/branchings. Perhaps they restrict themselves to what they see as certain. Perhaps they could only tell Rand that "To Live You Must Die", because that's as much as all the variants of this nexus in his future have in common... the rest of the circumstances are... fluid... but they saw that in no variant he can survive TG without "dying", whatever they really mean by that.

Anyway... Moiraine didn't know that, and she already got her answers back in Tear. It's only afterward she learned Rand went in there and managed not to be punished. It was too late for her.

In ToM she spoke of having wishes fulfilled, but no mention that she was offered a new round of three answers (and given that the Doorway ter'angreal are programmed to work only once per person, it sounds very unlikely that you can get answers or wishes twice).

The answers she got back in TSR may very well be revealed and turn out relevant, but it's a bit hard to see what motivated Moiraine not to give Rand answers and questions before the docks (or in her letter to him) if what she asked would help him, and knowing the possibility she would return was slim.

She also told Rand that what little more she knew of what happened in the world after she was gone did not concern him. She can't lie. I think one of Moiraine's questions resulted in her change of attitude with Rand. I think a question about him gave her a riddle that she solved only later. I think that's what her elusive answer to Egwnee about remembering how you guide saidar was all about. I don't think she dared ask anything about the Shadow or the LB. Her comment to Rand offering to help him puzzle out his answers kind of suggests Moiraine herself got riddles with no obvious meaning....

I think Moiraine herself won't even know she is so vital to Rand. I think the first clue we're gonna have is when, because Moiraine is now back again, Min finally reveals to Rand what she's seen exactly about Moiraine. I think this will be... cryptic.

Part of what makes me believe Moiraine isn't aware she is holding information/knowledge or something else altogether (it may be something she decides to do, not something she knows) which is vital to Rand is that if Moiraine knows she'd tell Rand the minute she sees him, and Brandon has long revealed the reunion isn't far ahead now (Merrilor at the beginning of the book, almost certainly). It sounds too early to reveal how Moiraine is such a key.

Some think Moiraine's "crucial role" isn't even related to the endgame as such, but she will break an important "block" or obstacle in front of Rand long before that, very soon in fact. Those often suggest that Moiraine's role (Mat will arrive last, most likely) will be the key to avoid a new "Fateful Concord", that Moiraine is the one who will tell and convince the Aes Sedai to remember that you can't force Saidar to do anything, that you can't even get to touch saidar without first surrendering to it. Without surrendering first, you have no power. Moiraine will tell of her surrendering to Rand, and of her surrendering to the Will of the Wheel which brought her here now. She put her faith and hopes in that, she embraced the dark and painful future the Wheel had put in front of her, made the sacrifice because it's what she had to do, The Will of the Wheel... and here she is back at Rand's side on the eve of the LB, as she always wished she'd be. This is an explanation Egwene is already familiar with, as well as in how Moiraine applied it to herself and Rand. All too familiar with... And it combines what Moiraine told her in the Waste with the wisdom from the WO about embracing pain she gained in TGS. The pain Egwene (the world) needs to embrace now is the LB. She/they can't let her fear of pain hold her back or break her or her spirit and will to win, the time has come to face Shai'tan, to embrace that pain and be stronger than Shai'tan. What she has to surrender to is of course Rand and her instinct to try to force him into the decisions she thinks he must make, not those he feels he must make. The only way the Tower can play its role in the LB, the only way the world can help Rand in the LB is by understanding they are the banks, but he is the river. Will always be the river. They can guide, not force. Before they can have their say in how the events proceed from now, they must surrender.

So Moiraine's speech, or quite possibly private conversation with Egwene, at a time where everything at Merrilor is blocked, could be the key. I could go something like this... Moiraine arrives to Merrilor a few days late, she is brought to Rand. Min's so relieved she's alive she immediately share her viewing of Moiraine/Rand and how without her he was almost certain to lose. Moiraine is baffled and has no idea how she could be so important to Rand. She may disclose her answers from the Finns... (good opportunity to speak of the Finns stuff when Moiraine tells her story to Rand and the others) to show how they hold nothing that could be described as "vital" for the LB. She learns how things stand at Merrilor, how Rand is incapable to sway the Amyrlin, and how most of the leaders stand with her, when he feels the Wheel is pulling him to break the seals, but not without first making this alliance of the Light. Moiraine learns the Amyrlin he speaks of is Egwene, she expected Elaida, and then she understands what she must do.

But I'm quite undecided. My feeling is that it may be something else, related more to the endgame, and Moiraine will spend most of the AMOL alert to any sign of the Wheel pulling her to some decisions/actions, having no idea what she is meant to do. That would be quite a new challenge for her. OTOH, the theory above probably brings things full circle much better, in the end Moiraine becoming the last piece of the puzzle for the world gathered at Merrilor to "embrace" Rand as the Dragon at last, to place their faith in him.