Which among the following compounds converts alkyl halides to nitro alkanes?

Which of the following compounds gives the same $S_N1$ and $S_N2$ product?

Arrange the leaving group ability of the following groups in decreasing order:
$(I)$ $CH_3-C_6H_4-SO_3^-$,$(II)$ $C_6H_5-SO_3^-$,$(III)$ $N_3^-$,$(IV)$ $Br^-$

Given below are two statements:
Statement-$I$: High concentration of strong nucleophilic reagent with secondary alkyl halides which do not have bulky substituents will follow $S_{N}2$ mechanism.
Statement-$II$: $A$ secondary alkyl halide when treated with a large excess of ethanol follows $S_{N}1$ mechanism.
In the light of the above statements,choose the most appropriate from the options given below:

Which one of the following compounds is inactive towards $S_N1$ reaction?

What is the relative rate of $S_{N}1$ reaction for $(CH_{3})_{2}CHBr$?