Ok then, I'll try to propose a vote:
[X] Plan Micromanage:
-[X] Try to balance your debts and responsibilities.
-[X] Keep to answering question, with but a few things that you raise as of interest.
--[X] Tell them that Ulthar is heir now, and about his character, but merely say that there was downright human unpleasantness around the whole matter and that as dwarves, the whole thing is a massive pot of shame best left unmentioned and untouched.
--[X] Share what you know of Belegar on a surface level, but keep back about his crisis of faith. Do mention he is unortodox and it has caused friction with more elderly clans/holds.
--[X] Don't mention the rift directly, personally, but warn him you witnessed a moment where a dwarven civil war might have happened, without going into the details. And that you'd like to stop something like that from happening, if possible.
--[X] Do talk about the rift between the holds, but talk about it as a Young/Old holds kind of thing, with Belegar and the High King as focus points. As competing theories of what is proper, culturaly and martially. Hint that there is more to it, but under the kind of seals that would make dwarves go to war to protect. War on the whole Empire, possibly.
---[X] Do go into the non-classified/non-privileged, general information on what the stances are between the two main currents. The Old and the New.
---[X] The golem (without the five-soul runes detail), and how dwarves in general are about old things is definitely insight the top Empire diplomat wants to have, if they don't have it already. Just put it in more general, less personal terms if he asks.
--[X] Do mention the canal project, if he is unaware, he needs to know.
--[X] Don't talk about the We directly, that should be their choice first, but do mention that the slik situation might be suffering some major disruptions soon from K8Ps.
--[X] The Dragon and its ceasefire. Dragons fly. The Empire should know it's there, if he asks. Otherwise, you should inform your boss.
--[X] Mention your Thane status and it's implications as you understand it. It shouldn't matter, but you're not the top Empire diplomat. He might know some way to use it.
--[X] Don't share dwarven language with him. That's secret/earned in person. Do share insight into general dwarven culture and behaviors, as long as it is scrubbed of personal details and couched in general terms.
--[X] Do tell him details about other noble dwarves, their opinions and preferences. Anything public, at least. If things were said in confidence, only use them in non-personal ways. IE: I've noticed some dwarven organizers struggle with working with humans because of how different the problems that come up are, between the two species. You can hint without outright saying things. He's a diplomat. This should be bread and butter for him.
Really, if this was anything but diplomacy, I'd trust Mat to handle it. As it is, I'm not sure if this is helping or hurting, but I think going in there already committed what you will and won't reveal if asked is a good idea.