Also- and note that this piece of @Lunaryon 's is basically my first exposure to Inuyasha- I suspect that that our ambivalently friendly yokai (?) is the type to get suspicious, bored, or both if we give him a long backstory monologue. Especially when, well, bat-demons all over the place.
He might, or he might not. Since we don't know that he can detect lies reliably, especially through a "pretty good" glamour, we shouldn't deliberately tell him improbable stories in the expectation that he'll be so confident that we aren't lying.
If nothing else, there's no benefit to doing this now, as compared to doing this later when he will presumably be no less capable of spotting a lie.
1. Plan: So essentially you're saying "broad sweeps now, everything after the current battle is over"?
I think I can agree with that.
If we're going that route, I think my side comment about the Dark Kingdom's mana containment technique bears mentioning before the battle (Dark Kingdom bases seem to fairly consistently have one, and if Kagome or Inuyasha can spot it, it would help the team track down the source of the problem).
Our lack of an information gathering network, and the fact that the Dark Kingdom isn't the only group able to use the mana containment barrier (so its presence isn't a guaranteed sign of their involvement), are strategic information, rather than tactical information, so they can wait.
2. Yokai: Japanese uses a very different writing system than English, and it doesn't use exactly the same phoneme palette anyway, so the spelling of Japanese loanwords in English is inherently somewhat variable (or at least inherently subject to debate). I've also seen it spelled "youkai."
The closest
translation is probably either "spirit" or "fey / fairy". "Demon" is sometimes used (and I think the Inuyasha dub used it), but "demon" is only a fair description of some yokai, not all.
Unless you're talking about Inuyasha specifically, in which case I'm pretty sure he's only half yokai (specifically a dog yokai) on his father's side, with a human mother (I think she got killed by the dad's enemies before the start of the series, though).