Yes and no. You're extremely unlikely in modern days in developed countries end in a situation where going vegan would jeopardize your chances of survival but survival still major, if not one or the most important values for vast majority of people. If you were forced for an example between dying and consuming animal product or regular consumption of animal products I doubt most vegans would chose to die. I mean after all we still harm animals by many of our actions while knowing those actions bring harm but are necessary to our survival or advanced highly beneficial way of life and vegans don't exactly kill themselves over the fact.
As for questions they are fairly easy to answer to me (except maybe personal ones), as we lack nuance and details concerning scenarios that would make them difficult and we forced to chose between, in those cases I will have to rely on heuristics, knowledge and statistics regarding factors like utility, length of life and violation of morals.
1. Child is obvious choice here, a child is far likely to live longer and have entire life before them and likely has greater potential on information given as all we are given regarding another person that they are impaired in terms of eye-sight and paralyzed in some capacity.
2. I don't personally own a puppy and a cat so it wouldn't be personal decision based on my attachment to it. I would have make decision based on other factors. Cat is less expensive (at I suspect it's at least food wise) and requires less effort to maintain than a dog (unless perhaps you own backyard/front yard but cats are obligatory carnivores while to my knowledge at least some types of dogs are capable to adapt to a vegan diet what would spare me of funding various animal agriculture industries. So, puppy I guess.
3.Hmm statistically speaking black people are more likely to commit crimes, especially more severe ones. However, statistically speaking also men are more likely to commit crimes, at least violent ones than women. I would have to actually check it up how black women do against white men crime wise. However, given criminals make only small fraction (% wise) of society that person is far more likely to not be a criminal (at least not found guilty in court of law) and black people tend to be poorer by large margin meaning likely their contribution to the society is likely lesser going of by typical indication of income representing more important or/and scarce tasks in society than that of a white person. So likelihood of greater utility would favor white men.
4. Same situation as with dog and cat but I can't really answer such question as it lacks relevant factors and data for to make a judgement that would favor one over another. It would really be circumstantial depending on the case. I could pick my lover or my sister depending on nature and quality my relationship with each. Inconclusive.
5.Well, probability of survival of that child is so astronomically tiny that even given all factors that would advantage child over disabled person and fact they have 100 % of survival I would rule in favor of disabled person.
6. Are there even statistics or % of reformed rapists? Let alone rapists that no were not only not caught in some criminal activity but actually not being crappy people. However, one would have to take into consideration that friend is dying (is he just severely injured and without medical assistance he will die or mortally injured and he is finished?) and rapist could reform. If friend has some realistic chance of surviving then friend, in case of ensured death then still leaning toward a friend as I've way too little info on a rapist to know what I'm doing beside helping to survive dangerous and unethical individual over condemning what I assume is innocent friend of mine to die a horrible death in a fire.