Temperature profile at steady state
No, the temperature gradient is not uniform across all three layers.

To see why, start from the Fourier law for heat flow, shown in my solution to this problem. 

Since at steady state the heat flux $q$ must be equal for all layers, we have that  

$$q_{1}=q_{2}=q_{3}$$ 

And since the layers are equal in thickness, 

$$ k_1\Delta{T_1}=k_2\Delta{T_2}=k_3\Delta{T_3} $$

Clearly, if the $k$ are not equal, the $\Delta{T}$ cannot be equal either, so the profile will not be that in (1).