如图,在四棱柱\(ABCD-A_{1}B_{1}C_{1}D_{1}\)中,\(AA_{1}⊥\)平面\(ABCD\),\(AB/\!/CD\),\(AB⊥AD\),\(AD=CD=1\),\(AA_{1}=AB=2\),\(E\)为\(AA_{1}\)的中点.
\((\)Ⅰ\()\)求四棱锥\(C-AEB_{1}B\)的体积;
\((\)Ⅱ\()\)设点\(M\)在线段\(C_{1}E\)上,且直线\(AM\)与平面\(BCC_{1}B_{1}\)所成角的正弦值为\( \dfrac {1}{3}\),求线段\(AM\)的长度;
\((\)Ⅲ\()\)判断线段\(B_{1}C\)上是否存在一点\(N\),使得\(NE/\!/CD\)?\((\)结论不要求证明\()\)