May copying a particular statement be considered as a plagiarism?
Suppose, I have mentioned a standard definition of a mathematical term, exactly copied from a textbook, in my research article. May it be considered as a plagarism?


If the term is really standard, no plagiarism has been committed. But cite the source you got the definition from. Even such a standard term as the set of natural numbers can be introduced differently: either including zero or not. There are also notational reasons: as an extreme example, there are researchers in the wild who don't associate ℕ₀ with the former and ℕ₊ with the latter (or at least, they say they cannot parse these symbols and reject your paper on these grounds).


  Similarly, I use an earlier proved theorem in my article. I mentioned its statement exactly as it is stated in the original article along with its proper reference. May it be considered as a plagarism?


The same applies here. If the theorem is really standard, no plagiarism has been committed. Again, cite the source. Some theorems have subtleties (the zero, the empty set, up to isomorphism, etc.) which you understand only when you dig deep into the cited paper.