如图,在几何图形ABCDEF中,AB∥CD,AD=DC=CB=CF=1,∠ABC=60°,四边形ACEF为矩形,平面ACEF⊥平面ABCD.
(1)求证:平面FBC⊥平面ACEF;
(2)在AB上确定一点P,使得平面FCP∥平面AED;
(3)求三棱锥E-CDF的体积.