Measuring current using low side shunt method (MCLV-2 board)
(1) Is the simplified circuit correct?


Yes. It is a valid simplification of your 'original' circuit.


  (2) Are these equations correct? 


Yes (though they might be easier to solve if you define Vref as 'ground').


  (3) Do I need knowledge of V1' and V2' for solving this circuit?


No. The formula for a differential op amp is Vout = (V2-V1)*Rf/Rin, so you only need to know the voltage difference between V1 and V2. This voltage is determined by the resistance of R1 and the current flowing through it.  

NOTE: In your circuit current flows from V1 to V2, so Vout will go negative (relative to Vref) for positive current. However the MCLV-2 board's amplifier inputs are connected in reverse compared to your circuit, so their output voltages will not be inverted. Also the reference voltage is 1.65V (3.3V/2) not 1.36V.