解：?$(1)$?解不等式組?$\begin {cases}{-2x+2＜6}\\{\frac {3x-1}4≤2}\end {cases}，$?可得?$-2＜x≤3$?
∴不等式組?$\begin {cases}{x＞m-1}\\{x-1≤n}\end {cases}$?的解集也為?$-2＜x≤3$?
∴?$m-1=-2，$??$n+1=3$?
∴?$m=-1，$??$n=2$?
∴?$m-2n=-1-2×2=-5$?
?$(2)$?當?$m=-2$?時，不等式組為?$\begin {cases}{x＞-3}\\{x-1≤n}\end {cases}$?
∴不等式組有四個非負整數(shù)解，即?$0、$??$1、$??$2、$??$3$?
∴?$3≤n+1＜4$?
∴?$2≤n＜3$?
