Give the chemical reactions for the following conversions:
$(1)$ $m$-nitrobenzoic acid from toluene
$(2)$ $m$-chloronitrobenzene from benzene
$(3)$ $n$-propyl bromide from $1, 2$-dibromopropane

(N/A) $(1)$ Toluene $\xrightarrow[\text{Alkali, } \Delta]{\text{KMnO}_4, [O]}$ Benzoic acid $\xrightarrow[\text{Conc. H}_2\text{SO}_4, \Delta]{\text{Conc. HNO}_3}$ $m$-Nitrobenzoic acid
$(2)$ Benzene $\xrightarrow[\text{FeCl}_3, \Delta]{\text{Cl}_2}$ Chlorobenzene $\xrightarrow[\text{H}_2\text{SO}_4, \Delta]{\text{HNO}_3}$ $m$-Chloronitrobenzene
$(3)$ $1, 2$-Dibromopropane $\xrightarrow[\Delta]{Zn, -ZnBr_2}$ Propene $\xrightarrow[\text{Peroxide}]{\text{HBr}}$ $1$-Bromopropane ($n$-Propyl bromide)