Note that no other reagents are needed in order to complete any of these sequences, you should only be using what is there.
II The reaction of an alcohol with a hydrogen halide such as HBr is typically SN1 in character provided a reasonable carbocation is being formed. Here, thats means a resonance stabilised secondary carbocation. The two products arise due to the possibility of the bromide nucleophile attacking either of the electrophilic carbocations revealed by the resonance contributors.
III If an alkyl bromide is heated with strong base (here it's t-butoxide), then a 1,2-elimination to give an alkene occurs. Alkyl halide eliminations are typically E2. In this case the base is quite large so anti-Zaistev elimination is going to dominate.
IV Ethers can be cleaved by strong acids like HBr via an SN1 type reaction to give an alcohol and an alkyl halide. The selectivity is controlled by the stability of the intermediate carbocation.