(1) ∵直三棱柱ABC-A1B1C1,∴A1B1//AB,CC1⊥面ABC.

∵BF⊥A1B1,∴BF⊥AB.

∵正方形AA1B1B,∴AB⊥BB1，AB=BB1=2.

∵BF∩BB1=B,∴AB⊥面BB1C1C,∴AB⊥BC.

在Rt△ABC中，∵E为AC中点，AB=BC=2,

∴==·AB·BC=1.

∵F是CC1中点，∴CF=········CC1=BB1=1

∴=·CF=·1·1=.

(2)连A1E,B1E,A1F，则A1E==,A1F==3,

EF=AC1==

∴A1E2+EF2=A1F2,∴A1E⊥EF.

由(1)在Rt△ABC中,E是AC中点，∴BE⊥AC.

∵面AA1C1C⊥面ABC,面AA1C1C∩面ABC=AC,∴BE⊥面AA1C1C

∴BE⊥A1E

∵EF∩BE=E,∴A1E⊥面BEF,∴A1E⊥BF

∵BF⊥A1B1，A1B1∩A1E=A1,∴BF⊥面A1EB1

∵DE⊂面A1EB1，∴BF⊥DE.