Firstly, about (A), you are correct that two enantiomeric pairs are formed. You have misread the question, it says the INCORRECT option.
Then coming to why Cl2/hv reacts but NBS doesn't give its usual bromine substitution. As you already know, these reactions are free radical reactions that need a free radical initiator like light, peroxide, heat, etc. Cl2/hv has the presence of sunlight that is able to do the homolytic cleavage of the Cl-Cl bond.
NBS adopts the following mechanism.
The initiation step in allylic and benzylic bromination with NBS is the formation of a
bromine atom by homolytic cleavage of the N-Br bond in NBS itself.
Wondering where the Br2 came from? The image doesn't show that but HBr formed reacts with NBS to give N-Bromosuccinamide and Br2.
The unique role of NBS is to maintain the very low concentration of
bromine by reacting with HBr.The low solubility of NBS in CCl4 (<0.005 M) is important for bromination in NBS. Different solvents can show different reactions while it may be so that NBS all alone doesn't give any reaction until we have a free radical initiator. Hence, CCl4 must be used as the solvent in allylic or benzylic bromination (I mean not necessarily allylic and benzylic only) with NBS. During the reaction, the insoluble NBS, which is denser than CCl4, disappears from the bottom of the flask, and the less dense by-product, succinimide forms a layer on the surface of the CCl4. Possibly the further reactions occur at this surface (who knows!).
TL;DR NBS all alone won't give any reaction here. The presence of a suitable solvent is the key to its bromination.