Does turbulent flow have boundary layer ? Does separated flow have boundary layer?
Yes.
There are boundary layers (BL) in laminar flow, turbulent flow, and the 
transition between the two.

"Flow separation occurs when the boundary layer travels far enough against an 
adverse pressure gradient that the speed of the boundary layer relative to the 
object falls almost to zero. The fluid flow becomes detached from the surface of 
the object, and instead takes the forms of eddies and vortices."

From: "Flow Separation"
https://en.wikipedia.org/wiki/Flow_separation

Note that the shear stress at the wing surface drops to zero (or very close to zero) after the BL separates.

It is also possible for BL to re-attach to the wing surface after an initial separation. In that case the shear stress returns to a non-zero value.