DE=23，AF=23×2=43，

∵ Quadrilateral ABCD is a square with a side length of 2.

∴∠DAB=90，AE=2-23=43，

∴AE=AF，

△ AEF is an isosceles right triangle.

(2) The quadrilateral ABCD is a square with a side length of 2,

∴AD=BC=2，

When the point f moves to the edge BC and AE=BF,

And then DE=CF,

The quadrilateral EFCD is rectangular,

∴EF∥CD，

∫AE = 2-t，BF=2t-2，

∴2-t=2t-2，

∴t=43，

When t = 43, the line segment EF is parallel to DC.

(3) According to (2), AE=2-t,

∫CF = 4-2t，

∴AECF=2？ t4？ 2t= 12，

∵ quadrilateral ABCD is a square,

∴AD∥BC,AB∥DC，

∴△AME∽△CMF,△AMN∽△CMD，

∴AMCM=AECF= 12，

∴ANCD=AMCM= 12，

∴AN= 12AB，

∴ANNB= 1.