Schematics of PIN Photodiode interfacing with an ADC
Regardless of what Marcus Muller says, your circuit will work, as far as it goes. The circuit you show is not, in fact a current amplifier, but you don't want a current amplifier, so the question is moot. What you want is a current-to-voltage converter, and that's what you've got.


  1 What can I do with ground/case pin of PIN photodiode to improve
  performance? Currently, I have just grounded it.


That is about all you can do.


  2 I am using second op-amp as buffer. Is there any possibility of buffer
  getting unstable? What measures I can take?


Look at pages 11 and 12 of the data sheet. The AD8616 is unity-gain stable, which means that for most loads you don't need to take any special measures. An ADC does not normally have what is called a high-capacitance input. 


  3 I am included a capacitor in parallel with feedback resistor to
  compensate the pole included by capacitance of PIN diode. What other
  measures I can take to stabilize my interface circuit if I found any
  instability after I get my PCB done?


The most important thing you can do is done before you get the PCB made. Provide decoupling and a ground plane. Decoupling is done with a 0.1 to 1 uF ceramic capacitor (not a disk cap) from Vcc to ground as close to the power pin as you can put it. For a relatively high-speed op amp like the AD8616 and low signal levels, a ground plane is a must. 

I suggest that, once you have a pcb, tune the feedback cap. Modulate an LED with a square wave at about 1 kHz, shine it on your grating, move the grating until the detector is illuminated, and observe the op amp output. With a good square wave generator and a non-white LED you should be able to get optical rise and fall times below 1 usec. Look at the rising and falling edges with a scope set to about 1 to 10 usec/div. If the op amp is oscillating, or the rise/fall edges ring, increase the cap. If the edges are slow and don't settle quickly to final value, decrease the cap. In this way you can optimize your response.

If the optimized response is too slow, about the only thing you can try is to provide a bias voltage. Instead of tieing the PD anode to ground, connect it to a negative voltage of something like -5 volts. You will then be able to reduce the feedback cap and get quicker response. If you've designed your board with only positive voltages, like a single 3.3, you're just out of luck. Keep this in mind when you design the board.

If you don't want to provide a ground plane because of cost, fine. It's your choice, but performance may suffer, depending on how good you are at layout.

As you may have realized, it's a good idea to put the op amp as close to the detector as possible, as well as the summing-junction side of the feedback components, as close to the - input of the op amp as possible, in order to minimize total input capacitance.