1, which proves that PA is perpendicular to ABCD, so PA is perpendicular to CD. The angle PCD=90 degrees, so CD is perpendicular to PC. So CD is perpendicular to the plane PAC, so AC is perpendicular to CD.

2. By connecting DE, we can know that the angle of COS DAE = that of COSEAC * that of COSCAD = 1/2, and that of PA=AB=AC, then the angle of CAD =45 degrees, so we can know that the angle of CAE =45 degrees.

Establish a rectangular coordinate system with A as the coordinate origin, AC as the X axis, AB as the Y axis and AP as the Z axis. Let the normal vector of plane ABE be A (vector), the normal vector of plane ADE be B (vector), and PA=AB=AC=2.

Then there are: a coordinate is (0,0,0), b is (0,2,0), d is (2,2,0), and e is (1, 0, 1).

Vector AB* vector a=0 (1)

Vector AE* Vector a=0 (2)

Vector AE* Vector b=0 (3)

Vector AD* vector b=0 (4)

From (1) and (2), the vector A = (1, 0,-1).

By (3) and (4): vector b=( 1,-1,-1) (for convenience, it is not expressed as a parameter).

So COS (vector a, vector B) = [( 1, 0,-1)*( 1,-1)]/root number 2* root number 3 = the square root of 6/3.

So the cosine of dihedral angle B-AE-D is the square root of -6/3.