A doggy style position is within the range of standard sex. It is not paraphilia for sure. It is very common and probably as common as various woman-on-top positions.

Being choked is what they call kink now. I am not sure that it is paraphilia though. I am not even sure these things (what is kink, what is paraphilia, etc.) are well defined. I bet that different people would disagree on the definitions. So if for now we call choking a kink, then it is one of the more common types of kink. To sum up, her sexual preferences are not highly unusual. Also, the doggy style position is safe and nothing prevents you from having intercourse with her in that position. You might like it a lot. Choking presents safety issues and if she wants you to choke her, you need to read up on choking safely and/or talk to people about it. This is not something for you to do without extensive prep work - I am sure you knew this already.

That what she likes sexually is related to the rape might be a form of imprinting. If a baby duck sees a man and not his mother duck at birth, the baby would follow the man and not this mother duck because of imprinting. I guess you can explore root causes with her, or maybe if you have money for it, you can get the advice of a sex therapist, and yes, in light of the preference for choking, maybe professional advice would be a good idea. Other than that, I do not see what makes you so surprised. That she did not tell anyone? If you were raped by your cousin and you told other cousins about it and nobody believed you, you probably would get discouraged and not tell anyone. When you wonder why she did not tell ANYONE, what are the options for that SOMEONE in your mind? That she did not involve the police is because the perpetrator was a member of her extended family. Also, there might not have been proof as the rape was not brutal. Parents? Girlfriends? What would have been the point in telling them? She told you because she believes that this knowledge is relevant to your relationship. Alternatively, she made up the story because she feared that otherwise you would judge her past behavior negatively.

The troubling part here, in my mind, is not that she likes doggy style sex, but that you see yourself as her helper (a rescue fantasy). If you want her to be your girlfriend, tell her that, but do not try to help her. Not only is not clear where she needs help, but also should she need help, professional or peer support help would be more appropriate than your assuming the white knight role here.

I would say that if she cannot get an orgasm without choking, then there is more trouble and more learning for you to do than if she simply likes being choked but can get an orgasm without choking. In other words, given that this would be your first experience, if it is at all possible to delay your attempting to choke her, that would be the most prudent course of action.