You really can't conceptualize of women except in the most two-dimensional, stereotypical of terms, can you? Christine isn't a "tough girl." She did well in one fight sequence for a while and then got defeated. She's also not a "weak girl" or a "damsel in distress" -- she did well in that fight, and she held her own in hand-to-hand combat in "The Serene Squall," but she's also not a combat specialist and has her limits. She's just a reasonably competent officer who's not omnipotent.
Or, y'know, not. The writers could in fact follow the factual outlines of Christine's TOS backstory vis-a-vis Roger Korby without changing her personality to match the TOS version's (almost total lack of a) personality.
I mean, they've already had one tragic figure in Hemmer. I see no reason to have another.
It is possible; nothing about Nyota's sexuality has been established. We know that her Kelvin Timeline counterpart had a relationship with Spock (which in SNW would just feel creepy!), but that doesn't preclude her Kelvin Timeline self from being bisexual or pansexual. And the sexual orientation of her Kelvin Timeline counterpart tells us nothing about her Prime Timeline self.
Her long-time partner -- he was a man, but I don't think they were married -- tragically passed way during the hiatus between filming S1 and S2, actually. I don't believe she has publicly indicated that she has entered a new relationship; last time I reviewed her tweets, she seemed to be indicating she was still grieving her partner's death.