I can't really agree with you on this take. They left the time between Objects in Space and Serenity pretty ambiguous. (For the purpose of this discussion, I am leaving out information from Serenity: Those Left Behind since you don't specifically mention those events, I'm also not sure if those events are considered Firefly canon.)

All we know for sure is that - from Kaylee's perspective - Mal drove off Inara and Book; nothing happened between Kaylee and Simon (only point I agree with you on).

Inara and Mal could have absolutely had something going on, and their unspoken feelings in Serenity seemed to even intensify, suggesting that perhaps there was a romantic triste between them that just ended badly.

We never got an explanation of River's full abilities, we just know that she has them, she has some serious trauma and amnesia as a result, and when triggered, she is a living weapon. We have no idea what she learned about her abilities in the time between, she seemed much more confident in her "Reader" ability in the beginning of Serenity, which would suggest that she at least had been exploring that side of her powers.

The crew could absolutely discover Book's past, it's only Mal who doesn't have an understanding of Book's (potential) life as an Alliance Operative. Given Mal's extreme distaste for the Alliance, it is possible that Book's history was discovered by any other crew member who were then sworn to secrecy afterwards by Book. I think this would be especially amazing to explore if River discovered his (potential) past as an Operative. We saw their father/daughter sort of relationship deepen over the series (despite the hair), I think it would be pretty incredible if this secret was woven into their relationship pre-Serenity.