Diffusion across a thin film
(1) determine at which side substance A will diffuse out of the membrane
  
  
    should I answer at the right side or that the substance stays within the membrane?
  


Neither, because the concentration is higher in the membrane than either side, the substance will flow out of both sides initially at least. After a while the material will flow from left to right (high concentration to low concentration) and converge towards steady state.


  (2) chose one of the following profiles below which represents the concentration of a substance A at steady-state.


First thing - When doing diffusion problems immediately refer to Fick's laws of diffusion.

Fick's first law assumes a steady state system and is given as:

$$J = -c D\frac{dx}{dz}\quad \text{or more simply} \quad J = -D\frac{\Delta C(x)}{\Delta z} \quad \text{or more generally}\quad J = -cD\ \nabla x$$

Where $J$ is flux (mols through an cross-sectional area per time), $c$ is total concentration, $C(x)$ is the concentration at point $x$, $D$ is the diffusion constant, $x$ is the mole fraction and $z$ is position. 

For steady state to occur, $J$ must by definition be constant through the entire membrane and thus $-D\frac{\Delta C(x)}{\Delta z}$ must be constant through the entire interface. Since $D$ is already a fixed constant, we can assume $\frac{\Delta C(x)}{\Delta z}$ must also be constant. Thus the plot with a constant slope is the steady state profile which is B.

Q.E.D.