When you speak of k-species, you are talking about r/k selection theory with r and k representing two ends of the offspring spectrum. R-type species choose quantity over quality. They produce a maximal number of offspring, choosing to care for the individuals less and allowing the sheer numbers to propagate the species. Insects are a perfect example. K-type species choose quality over quantity. They produce fewer offspring, but the offspring that they do produce are larger and more complex and the parents take more personal care of them until they reach maturation. Humans are indeed a k-species. Being a k-species does not necessarily mean that there are no predators, but in the case of humans while wild animals can certainly kill us, our mastery of our domains keep up safe from other species.
I'm not entirely sure what the second part of your question means. It is impossible to know if any predators of humans will try to overtake us to survive in the long term, but so far humans have done an excellent job propagating our species. Various microbe-based diseases in the past wiped out entire populations, but we have a much greater knowledge of the microscopic world now and have eradicated many disease organisms.