Does diffraction pattern depends upon thickness of slit? I know that diffraction pattern depends upon the width of slit but does the thickness of slit also matters?
If so then what happens to the diffraction pattern at variable slit thickness?
 A: As soon as you ask such questions you are considering a real material situation, not an abstract one. Which material is the slit made of? Which particle is diffracted? The answer to your question is that the pattern depends on this and on the thickness of the slit. 
A: The answer is yes. How much depends on the details of the materials and sizes of the slit and in some cases how many slits and how close they are together. This is also of interest for small circular holes or patterns of holes rather than a single silt.
The math to work out the details is not easy but essentially you have a more complicated boundary layer problem than a thin slit. in short, rather than working a 2D problem, you have to consider all 3 dimensions.
If you think about it, if the hole is very long compared to the wavelength of light then it would act something like a waveguide and only modes that fit the size of the hole would be allowed to reach the other side.
If the thickness is somewhat comparable to the wavelength of the light and you plot the amount of light that is transmitted as the thickness of the metal film is increased you will find that the amount of light increases and decreases almost periodically.
If the metal is conductive, then the electrons in the metal can also be moved around by the electric field causing a group oscillation called a plasmon. This can enhance the electric field at the edges of the slit or hole. The edge on the other side of the hole can also act like a receiving antenna and sometimes this can let more light be transmitted than a calculation where there are no plasmons. This was a somewhat of a surprise to people in the late 1990's early 2000's.
A lot of the complications are local to the areas near the surface of the aperture (the near field) as you get farther from the aperture (in the far field) the effects are less noticeable.
But keep in mind that for both thin and thick slits you will still get diffraction, although the exact details of the intensity and electric fields can be different depending on where you are looking.
A: The answer is no.  The original DSE by Young was actually performed not with slits, he used a knife edge ... actually a card.  The card depth does not matter.
The intensity of the pattern may decrease as less light is accepted if the source is angular .... as opposed to coherent like a laser source.
What causes the pattern ... the most in depth explanation is Feynman's path integral.  According to QM light/photons prefer certain paths over others and the preferred paths tend to be ones where the path length is an integer multiple of the wavelength.  In the DSE there are no photons in the dark areas .... they all go to the bright bands.
