i'll answer what i can, and leave the rest for my more knowledgeable fellows!
if you arrive in koa (or hnl, for that matter) at 9.55pm, you'll be overnighting here for sure.
you CAN get to kauai from koa without going to the mainland, but i'm pretty sure you'll have to go through hnl, although i haven't done that recently. try both the hawaiian and the aloha websites, also check islandair.
aloha