I'm not sure that either of the claims you suggest are "likely" are likely. (I'm also quite sure that the conflict you implicitly suggest exists between evolution and Christianity is a mirage, but that's another matter.)
The theory of evolution in no way implies that human capacities are "limited to what is necessary for survival". Stephen J Gould and Richard Lewontin borrowed the term "spandrel" from architecture to describe what one might also call "side-effects", biological traits that were not themselves selected for but are necessary accompaniments of traits that were selected for. Any particular case will be controversial, of course, but perhaps I can mention one intriguing such question: whether female orgasm has any benefit of the sort that would lead it to be selected for. The philosopher of biology Elisabeth Lloyd has written several interesting papers on this question. There is also an answer in this same area to evolutionary arguments against the innateness of sexual orientation. (There are answers elsewhere, too.)
As for Christianity, I don't see why our knowledge would have to be limited to what God wants us to know. One might suppose God had given us certain kinds of cognitive capacities, and then it is up to us how to use them. Indeed, doesn't Genesis tell us that Eve eats from the Tree of Knowledge of Good and Evil? I don't think God had that in mind. Hence the Fall and all that follows, right? (I'm not suggesting we read Genesis literally here.)
That said, I think the very abstract point, that there are things about the universe we simply aren't equipped to understand, is pretty plainly true. There are obviously things about the universe that my cats aren't equipped to understand. They've got some cognitive abilities, but those are limited in various ways. I don't see why we shouldn't be different. Indeed, surely it would be most remarkable if we were not. Whether the mind-body problem in particular is beyond us is, of course, another question.