MOS transistor maximum current
I think the current through the diode and the current through the resistor should be the same, since no current goes in to the OP-AMp. Is this correct?


Yes.


  I also want to know how to find the maximum current through the diode and calculate it.


It depends on information you haven't provided. 

First, you need to know the maximum output voltage of the op-amp, which could be nearly equal to Vdd, or it could be 2 or even 3 V less. 

Then you need to figure out what the LED current will be when the op-amp is producing that output. That depends on information about the MOSFET that you haven't included in your questions.