Let's consider the first question: If reincarnation is about humans dying and their souls taking on new bodies, doesn't a net increase in human population size contradict it?
I will be addressing this only as a logical question. I am not attempting to provide an opinion on whether reincarnation is true or not.
If I can find a source that has some familiarity with reincarnation and who can provide an explanation that avoids this potential contradiction, then this logical argument against reincarnation loses its strength. My source will be Brian Weiss.
Brian Weiss is an M.D. who offers past-life regression and future-life progression therapy He writes about a similar question: (page 8)
One of the questions that comes up frequently is "Where do the souls come from since there are so many more people now than when the world started?" I have posed this question to many patients, and the answer is always the same: This is not the only place where there are souls. There are many dimensions, many different levels of consciousness where there are souls. Why should we feel that we're the only place?
Weiss asks his patients because they are the ones in the hypnotic state with access to information, assuming what they experience is real.
Weiss's answer, or rather the answer he received from his patients, doesn't remove the possibility that non-human animals could have souls. They may represent "different levels of consciousness" where there are souls. That means the second question about the ethics of non-vegetarianism would still have relevance if all this is true. However, that wouldn't logically contradict reincarnation, but only complicate ethics.
The main question is whether differences in population size logically preclude reincarnation. Weiss's answer shows that one can avoid a potential logical contradiction by assuming that there are "many dimensions, many different levels of consciousness where there are souls".
"Brian Weiss", Wikipedia https://en.wikipedia.org/wiki/Brian_Weiss
Weiss, B. L. (2004). Same soul, many bodies: Discover the healing power of future lives through progression therapy. Simon and Schuster.