Hello and welcome to JustAnswer!
If you are just replacing bearings you won't have to worry too much about measuring pinion height, this is for the pinion spacer. You should be able to put your old shim back in. All other measurements will have to be done when you put it back together. You'll have to set the pinion preload when you put the pinion gear back in and crush the new crush sleeve. You'll have to set backlash and side bearing preload when you go back together because you have to remove the carrier to get the pinion gear out.
The only way to get the carrier out is to loosen the adjusters. They preload the carrier into the housing. You could pry with a massive prybar and never get the carrier out if you don't loosen the adjusters. The new bearings won't be exactly the same as the old ones due to production tolerances, and you can't get the carrier out any other way, so the preload/backlash has to be set. You can get the tool for the adjusters at www.millerspecialtools.spx.com.
As for as other concerns, make sure you get the housing absolutely clean. Any debris left behind will chew up the gears and the new bearings. Make sure to get the lube channel for the pinion bearings clear, debris likes to hide back there. If you have a limited slip carrier you'll need to use friction modifier additive in the fluid when you go back together or you'll destroy the clutches.