The correct options are
A B is CuI and the colour is due to the presence of impurity
D Compound B and compound D are same
This is not a simple reaction but a mixture of processes taking place in the same reaction vessel.
First step:
CuSO4+2KI→CuI2A+K2SO4
Second step:
2CuI2A→Cu2I2B+I2
The precipitate appears to be a brown sludge because of the iodine. Iodine is sparingly soluble in water but it dissolves in the presence of I− ions to form a dark yellow/brown solution due to the formation of a complex ion. There is almost certainly some KI left to achieve this.
Third step:
I2+KI→KI3
If thiosulfate solution is used, then the Iodine is re-reduced back to Iodide and the brown discolouration disappears leaving the white precipitate of CuI.
KI3+2Na2S2O3→KI+2NaI+Na2S4O6
All of the processes 1, 2 and 3 are taking place simultaneously. The thiosulfate is just an added part to help illustrate the chemistry and, if necessary, help to obtain a clean sample of CuI.