I don't think we would get anywhere useful if we keep digging into Citadel politics right now. We would probably end up alienating Ryam.
Preliminary plan. Thoughts and suggestions?
[X] Ask about the Conclave (leaving out any of the following questions if Ryam seems unwilling to answer, better to have him as a potential contact than wary of an over curious stranger);
-[X] "I too fear that war may soon come to Westeros, for I have heard disturbing rumors about the upcoming Conclave of the Faith..."
--[X] Try to learn what Ryan may know of the Reach Fey and their dealings with the Tyrells, insinuating that a credible rumor has made its way to us that Mace might be considering a marriage between his daughter and a Fey king, one who would claim dominion on Westerosi soil. Of course, if the Citadel was unaware before, this handily introduces the rumor to them.
---[X] What is the Citadel's opinion on this matter, if he is willing to share such information with us? Could this lead to another civil war less than two decades since the last one?
----[X] Is it believed Most Devout Septon Kyle actually has enough support or popularity to convince the members of the Conclave to support the legitimacy of such a union?
--[X] Far more disturbing than vague rumors about Fey Lords and Tyrell ambitions, however, are the words and actions Brother Lucan, thought to be a Chosen of the Father Himself. He makes no attempt to hide his disdain for magic and those who would practice it outside the guidance of the Faith. Worse still, he seems intent on rebuilding the Faith Militant and instigating a return to a more pious time. A civil war would be unpleasant for all involved, but a holy war would be disastrous for Westeros.
---[X] Are we making a mountain out of a molehill, or is this something the Citadel also fears happening? War can be good for certain types of business, but it is terrible for the people as a whole, and we would much prefer the people remain alive and able to trade untroubled by the specter of war and death.
----[X] Does Brother Lucan have enough support among the Faith and nobility of Westeros to potentially realize his goals?
-[X] What role, if any, does the Citadel expect to have in the upcoming Conclave?