Statements:
Some Vanilla are Strawberry
No Strawberry is Mango
All Mango are Chocolate
Only a few Pistachio are Mango

Some Pistachio are Chocolate: All Mango are Chocolate. Only a few Pistachio are Mango means some pistachio are Mango and some pistachio are not Mango. Thus, the pistachio which are Mango can be Chocolate. So, conclusion I is true.
Some Vanilla can be Pistachio: As there is no direct relation between Vanilla and Pistachio. Thus, there is a possibility that some Vanilla can be Pistachio. So, conclusion II is true.
All Chocolate are Strawberry: No Strawberry is Mango. All Mango are Chocolate. Thus, all chocolate cannot be Strawberry. So, conclusion III is false.
Hence, Only conclusion I and conclusion II follow.