The first question, AB=2AD=2, AD=A 1B 1= 1, BD=√3.

You can get BD⊥AD.

And because of D 1D⊥ plane ABCD.

So BD⊥DD 1

AD and DD 1 intersect at point D.

So BD⊥ plane AD 1DA 1.

So there is a conclusion.