So angle CAE= angle AEF,

Because AE equals EA, ce equals af, and angle CAE= equals angle AEF,

So triangle ACE and triangle EAF are equal triangles,

So AC=EF and AC//EF, so ACEF is a parallelogram.

(2)ACEF can't be square.

Because if ACEF is a square, the angle ACE is equal to 90 degrees, and the angle ACB is equal to 90 degrees, then point E is on the straight line CB and point D is on the straight line CB, then DE can't vertically divide BC? So the quadrilateral ACEF can't be a square.