You're forgetting that Chekov doesn't have a brother in the Prime timeline. Sulu definitively says in "Day of the Dove" that Pavel is an only child. It's what makes Kirk realize that the alien is inventing memories in order to increase the conflict with the Klingons.
And you'd take Sulu's word over Chekov's own... why?
In any case, the man named Chekov in the prime timeline and Pyotr in the new one might have had a kid brother in one timeline but not the other, due to the Nero effect. But since the worst the Nero effect has ever done to an established character is changing the color of his eyes, I sort of think there was a young Pyotr in the prime timeline, too, and just grounds for Chekov to go hunt for Klingons in "Day of the Dove", * or no *.
Not possible. Spock was already on the Enterprise when Kirk was at the academy. See The Cage.
That's no obstacle, as the meeting at the Academy in STXI is while Kirk is a cadet (of rather vague commission status, but apparently of Lieutenant rank) and Spock is a commissioned instructor one or two grades his senior. The similarity sought in the prime universe would not be "they were classmates", but a situation in which both would meet at the Academy grounds.
...Which is certainly possible even if the Chris Pike of "The Cage" weren't in any way related to the Academy, and almost inevitable if Pike in the prime timeline were a recruiter just as he appears to be in the new timeline.
No. Spock was rebelling against his father.
It's not as if he would outright say so. And even if he did, we know that Vulcans are lying bastards all, or at least constitutionally incapable of confessing to their true motivations.
Not likely. Doctors don't go to Starfleet Academy.
Says who? McCoy in the new timeline certainly went, after having completed his medical studies (and a fair deal of practice). We don't know if he wanted to become a military doctor, to capitalize on his past training, or merely a soldier wanting to forget it all - but everything is consistent with the former. We know for a fact that certain Trek doctors did attend the Academy, and the only uncertainty is on whether they conducted their medical studies there or elsewhere or both.
An animal slave woman as a Starfleet officer? Not bloody likely.
Why not? Starfleet would pride itself on being a refuge for the downtrodden - later it would receive Bajoran rebels and wayward Klingons and whatnot, for great propaganda value. It wouldn't be much different from the RAF taking Polish pilots under its wing: few would originally believe in these uneducated simpletons having any combat worth, but hey, isn't it great these lads carry on the fight against Germany?
As for the "animal slave woman" thing, we don't really know what the distinction is. Are certain women slaves to Orions? Are certain Orion women slaves? Is this because they are animals, or are certain slaves turned into animals? What does animal mean? Is it an insult, a description of profession, a description of biology, or what? TOS, TAS and ENT all contributed to our knowledge of the species, individuals or profession, but still not enough to even determine which of these three we're actually talking about!
Timo Saloniemi