已知\(\{a _{n} \}\)为等差数列，前\(n\)项和为\(S_{n}(n∈N^{*})\)，\(\{b _{n} \}\)是首项为\(2\)的等比数列，且公比大于\(0\)，\(b _{2} +b _{3} =12.b _{3} =a _{3} +a _{5}\)，\(b _{6} =S _{11} -2\)．
\((\)Ⅰ\()\)求\(\{a _{n} \}\)和\(\{b _{n} \}\)的通项公式；
\((\)Ⅱ\()\)设数列\(\{c _{n} \}\)满足\(c_{n}= \begin{cases} a_{n},n∈N^{*}\text{且}n\neq 2^{k} \\ lo g_{ \frac {1}{3} }^{ a_{n} }\cdot lo g_{ 2 }^{ b_{n} },n=2^{k},\end{cases}\)，其中\(k∈N ^{*}\)，
\((i)\)求数列\(\{c_{2^{n}}\}\)的通项公式；
\((ii)\)求\( \sum\limits_{i=1}^{2^{n}}c_{i}\)．