(a) I is a benzylic halide, thus, it undergoes SN1 reaction easily as benzylic carbocation is resonance stabilized. III also follows SN1 mechanism as it is 3$$^\circ$$ alkyl halide.
(b) Compounds I and II are 1$$^\circ$$ alkyl halides, then they undergo SN2 mechanism.
(c) Correct. In SN1 reaction, the nucleophile approaches the substrate carbon from the back side with respect to the leaving group. Nucleophilic displacement of the leaving group in an SN2 reaction causes inversion of configuration at the substrate carbon.
(d) Stability of carbocations follows the order:
$$\mathop {2^\circ \,benzylic}\limits_{(IV)} > \mathop {3^\circ \,alkyl}\limits_{(III)} > \mathop {1^\circ \,benzylic}\limits_{(I)} $$