" That might be a good idea, Agasha-sama. I assume - hope - at least an outline of the garrison's manpower needs will have been drawn up by someone who knows whatever it is someone is pointedly not telling us ."
Khenbish - no. She used her last round action on a second Endear objective with Chinatsu - leaving her an actual potential friend instead of just well-disposed. That may change your plans, since a 5-momentum check (getting to see Hirohide) is likely to need more than 2 actions (I guess Fire stance might help for the juicy bonus successes...)
Umeko/Khenbish - persuading someone in the stables to provide horses for you - and Matsu Tomuko - is probably water/courtesy. That would be TN3 and contribute to the Endear objective. 2 momentum is required to complete it.
Umeko - Brainstorming with Yokoi - who'd be happy to provide unskilled assistance since he'd benefit from the information too - is Theorise (Fire)/Government at TN3, but with +1 rolled ring die and +1 kept die and contributes to the Gather Information objective. 2 momentum will complete the objective.
The check about the Yasuki rumour was reason (earth) commerce.
If you're talking to Tomuko as well know, you can also try the TN2 earth/culture to recognise the mon on her swords.
You...probably....know who the Tsume are, since they're by far the most visible of the Crane's vassal families at the moment. Assume you know the name and they're a Doji vassal family (but no more than that) regardless - Pass a TN1 earth/culture to be assumed to know any elements of family description from Wedding at Kyotei Castle or Emerald Empire (note that at this time Tsume Takashi is Daimyo and his betrothal to Shiba Itsuyo is 'in negotiations')