Differential Service
Differential must be adjusted to specifications when changing the Ring & Pinion or when rebuilding it. Yet, in USA and Australia it is faster and less expensive -- and more reliable -- to replace with a good used differential than it is to rebuild one. Many rebuilds have not turned out well. However if you are good with detail, have the proper measuring tools, or use an expert mechanic a rebuild can be done.
Overview
NOTE: "pinion bearing adjust spacer" (crush sleeve) is NLA, yet needed for a proper rebuild -- even for just changing the gears.
Common Problems
Whining
I would not worry about a slight humming from the differential. Many of them do that. As long as you keep the oil level full, it should get no worse.
However, severe humming (whining) cause by a loss of oil will not go away. If you reset the gearset to the proper clearance and properly lube it it will work OK but will never be quiet again.
Knocking/Grinding
Knocking is caused by a worn part (probably a bearing) which must be replaced. It could be a side bearing or the pinion bearing.
It could also be caused by a chipped gear tooth.