When I cite an author of a previous study in the discussion of data results because my research results corroborate or negate his or her study's findings, is it necessary, that i should already mentioned such study in my review of literature?
In APA format, that is acceptable. The Introduction/Review touches on major points and all the points necessary for framing the study. But sometimes you get 'surprise' results or patterns that warrant an additional citation and reference.
Long(er) answer: on the one hand, this is done all the time (if you look in concurrent publications). One caveat however: this is more typical of longer publications. Therefore, I suggest (though, as I said, it is not a MUST) that you look and see if it is relevant enough to be included when you re-draft your Lit Review.
Yes, you can cite a new study/author in the results and discussion portion of your study, even if such is not mentioned in your review of literature. However, it is important to explain why that particular study/author is relevant to your research, and how the findings may impact your results and conclusions.