已知\(f(x)={{(2x-3)}^{n}}\)展开式的二项式系数和为\(512\)，且\((2x-3{)}^{n}={a}_{0}+{a}_{1}(x-1)+{a}_{2}(x-1{)}^{2}+···+{a}_{n}(x-1{)}^{n} \)

\((1)\)求\({{a}_{2}}\)的值；

\((2)\)求\({{a}_{1}}+{{a}_{2}}+{{a}_{3}}+\cdot \cdot \cdot \cdot \cdot \cdot +{{a}_{n}}\)的值；

\((3)\)求\(f(20)-20\)被\(6\)整除的余数．