There should be a tag under one of the bolts on the front cover. If it is there, that is how it was built new.
As it sits, lock one hub and try to turn the driveshaft yoke. Doesn't want to turn, there is a limited slip. Does turn, open diff. Count the number to turns the pinion yoke takes to rotate the unlocked U-joint 2 times. For the limited slip, go back to unlocking the hubs and how many pinion turns for one turn of a wheel U-joint (they will both be moving).
Check the condition of the oil via the fill plug. should look like oil, not a milk shake. Milk shake, chocolate pudding, that is water contamination. Can't answer how bad it is.