∴FD=AD,BE=AB

AD = BC，AB=DC

∴FD=BC,BE=DC

∠∠B =∠D，∠FDA=∠ABE

∴∠CDF=∠EBC

∴△CDF≌△EBC, so ① is correct;

AF = FD，AE=DC，EF=CF

∴△EAF≌△CDF

∴∠CDF=∠EAF, so ② is correct;

∠AFC=∠AFE+∠EFD+∠DFC，∠AFE+∠EFD=60

∴∠AFC-∠DFC=60

∴∠AFE=∠DFC

∴∠EFC=60

Similarly, ∠ FEC = 60

CF = CE

∴△ECF is an equilateral triangle, so ③ is correct;

In the equilateral triangle ABE,

The bisector of the top angle, the midline of the bottom, the height and the perpendicular bisector of an equilateral triangle are the same line segment.

∴G is not the midpoint of AE, and CG⊥AE cannot be verified, so ④ is wrong.

So choose B.