A differential is a bad place to learn how to fix cars. If you have a constant whine that is unchanged with load then you probably have bad carrier bearings. It the noise changes when you let off the gas it is probably pinion bearings.
Pinion bearings are NOT just tightened to a torque. They are tightened till the crucsh sleeve is crushed to such an extent that the bearings are tight enough that is takes 10-15 inlbs to turn the pinion. The only torque involved is the rotaional torque necessary to turn the bearings which are not now freewheeling. Very critical adjustment. This also must be done without the carrier present as the load of turning can only be the bearing supported pinion shaft.
The carrier bearings are shimmed to get their preload and are then checked the same way (force to turn). Once these perpendicular axises are established both the distance into the ring by the pinion (pinion depth) and backlash must be measured and adjusted possibly redoing both previous settings.
Usually one can replace the bearings without massive shim changes on the pinion. Its almost impossible to change carrier bearings without reshimming.
Bosch Master, ASE Master, L1
33 years MB technician