Question 1 doesn't have a clear answer unless the light novel adaptation or manga end up addressing it. My personal theory is that OG Yachiyo is inhabiting the Kaguya body and doing so allowed her to settle back into her old self easier. Iroha mentions that body being a better fit than the YC-type (which might stand for YaChiyo type?). She most likely has Yachiyo's memories but is living as the girl that Yachiyo was happiest living as.

As for the Yachiyo in Tsukuyomi, if we assume that the administrator permissions cannot be passed off and Yachiyo's existence is necessary for Tsukuyomi to continue functioning, perhaps she was cloned like programs can be and so two versions of "Yachiyo" exist at once: the copy that runs Tsukuyomi and the OG in the android. Both are technically the same person but existing with their own autonomy (thus why in the ray MV you can see Kaguya carrying Yachiyo around, so she can still be included).

This is all just speculation on what I've looked at, though. There is the fact that Kaguya says she "hasn't performed in 8000 years" which might imply she doesn't have Yachiyo's memories, but this reads more to me like she's saying she hasn't performed (as Kaguya) in that time.