In the following reaction is E2 or Sn2 favorable?
This is simply wrong. The person setting this question has assumed that the hydrazine will be completely selective for the ketone over the alkyl bromide and that the strong basic conditions will also cause elimination of the Br- to give the styrene. Selectivity seems most unlikely give the typical forcing conditions used in W-K reductions

Hydrazine is a powerful nucleophile and reacts with alkyl bromides under mild conditions often giving polyalkylation reference here. 

I consider it most unlikely there will be any selectivity unless confronted by literature example.