∵ quadrilateral ABCD is a square,

∴AC⊥BD，

∵PD⊥ plane ABCD, AC∈ plane ABCD,

∴AC⊥PD，

∫PD∩BD = D，

∴AC⊥ aircraft PDB,

∫AC∈ plane ACE,

Aircraft, ACE⊥. Aircraft.

2. link EO,

To sum up, the AC(O)⊥ plane PDB,

∴ < AEO is the angle formed by AE and plane PDB,

AB = AD = PD = a，

∴BD=√2a，

PB=√(a^2+2a^2)=√3a，

BE=BP/3=√3a/3，

On the plane PBD, EF⊥BD, vertical foot h,

EH/PD=BE/PB= 1/3，

∴EF=a/3，

OB=BD/2=√2a/2，

BH/BD=BE/PB= 1/3，

∴BH=√2a/3，

OH=OB-BH=√2a/6，

OE=√(OF^2+EF^2)=√6a/6，

ae=√(ao^2+oe^2)=√(2a^2/4+6a^2/36)=√6a/3，

∴cos<； AEO = EO/AE =(√6a/6)/(√6a/3)= 1/2

The angle between AE and PDB plane is 60 degrees.

3.∫DF// plane ACE,

And plane DFB∩ plane ACE=OE,

∴DF//OE，

O is the midpoint of BD,

∴OE is the center line of △BDF,

∴EF=BE=PB/3=√3a/3，

∴pf=pd-ef-be=pd-2be=√3a-2√3a/3=√3a/3.