If I can offer some advice to help you understand where Akiko is coming from:
1. Kotori did ask for help on her mission. We are the help she received.
This is a matter of perspective. The Asamoya is the only ship going on this potentially dangerous assignment where help would be unable to reach them if things were to go wrong. That strikes Akiko as quite odd, if not suspicious.
Kotori just revealed at the meeting that she went alone with Miharu once before, into a tremendously dangerous situation. Why was that necessary? It was a one-in-a-million shot that miraculously worked. Why is she doing this
again?
One time, you can call it dumb luck, two times suggests a pattern of recklessness/lack of foresight for danger that is unbecoming of Kotori's experience as a leader or hints at something more suspicious: a clear interest in Kotori not wanting Yamataian 'brass' to get involved at all.
If this is true, then what is she hiding? Everyone knows Yamatai can spare a patrol to protect a princess... unless there was something else that nobody is aware of...
Yeah, there's something to be said for SAINT agents being really good at undercover work and feigning ignorance for the benefit of fooling those crew not in the know. But that's not what it's coming off as to me.
I'm happy that you read into it like that because that's exactly what Akiko is doing. If she can come across as a skeptical, though concerned, crew member she can make her job as a spy much easier. It could force Kotori to reveal more information to assuage the crew's concerns. It could force the princess to reveal a different side to her than what she's offering now.
Kotori wears a very ornate mask. Opportunities to peek under or make a few cracks in it are few and far between.
Forcing Kotori out of a comfort zone gives the spies on the ship potentially invaluable information on Kotori's mind and how she processes things. Perhaps, even, it could show how much Kotori distrusts Yamatai as a whole. Remember, one of the primary objectives of this mission is to find out how close to 'betrayal' Kotori is to the empire. This line of questioning prods at that without being too suspicious or brazen.
Reika can't initiate these things on her own because she took the bullet, so to speak, and came out in the open as a SAINT agent, so it's up to Akiko to stir this pot so that Reika and the captain can glean the data from it.
Undercover spywork is hard to write, as it requires a lot of discretion, and I'm trying to show Akiko as being good at it while also being the weird, quirky person she is. Otherwise, she looks incompetent. I mean, sure, I could write her snooping around and 'getting down to business' more often, but that's highly unlikely because the Asamoya's MEGAMI can see all. So Akiko has to work very subtly and that requires her completely selling herself on her character.
So please don't take it as an insult to Saiga or anything. Akiko has to be like this to do her job. I know it makes things a bit hard on you as a player to reply to without making Saiga look like a jerk, but hopefully this post can help you a little.
Please try your best, though, because chances like this are not so common. I really appreciate you not blowing off the character, though, and coming to the OOC instead.
2. We're training against fake Shadow Vipers not because we expect to face them but because they represent a worst case scenario.
Akiko's reasoning for this questions follows a lot of what I just wrote before. We wouldn't have to prepare for a 'worst case scenario' if we had ample assistance. Akiko also wants to spread a little bit of discord and fear into the crew about the mission (hiding it as genuine concern, of course). Heck, in a best case scenario, it could make the entire crew a bunch of inadvertent spies with the gossip that results should more weirdness happen. It makes for great potential RP, too.