No, limestone is a sedimentary rock, not a living organism.
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b
Certainly a living organism
Everything that are living are living organisms. Every other things are not considered to be a living organism e.g. viruses.
I have known some people whom I considered walking talking turds, but technically, feces is not a living organism. It is organic matter, and it contains microorganisms, but it is not an organism.
because it is living or alive.
the question is unspecific every living thing is considered an organism
It would not be considered a living organism because it does not carry out several of the qualifications needed to be considered alive, including feeding and reproducing. It is, however, part of humans who are obviously considered living organisms and also consisting of cells, which are living organisms.
Viruses are not classified in a kingdom because they do not possess all the characteristics of living organisms. They lack cellular structure, cannot carry out metabolic processes on their own, and cannot reproduce without a host cell. As a result, they are often considered biological entities that straddle the line between living and non-living.
HIV is a virus, and since viruses require another organism to carry out the functions that would classify it as a living organism, it's considered "dead," that is until it finds a host.
Anything that is not considered to be a living organism. If it was never living (like a rock), then it has no DNA. All living beings have DNA. Viruses however, are not considered living because they do not have DNA.