the swap is exactly as the write-ups tell you. all straight forward and easy enough to do.
go ahead and do both sides as well as the bearings while you are in there. it's best to just get it done and have the peace of mind. gear oil is around a hundred bucks alone.
as far as the pinion shaft goes, i think i left mine out during the swap. it is just to make sure the spider gears don't pop out in case the diff spins. keep the truck in drive and don't go banging on the diff in any way and you should be fine but if you're nervous about it, go ahead and just put the pinion shaft back in. no need to bolt it back up at this point or anything.
whatever gear oil floats your boat will do. if you have the limited slip differential ADD FRICTION MODIFIER. I don't care what any of the oils say, you will need the friction modifier in a l/s diff.
hope i answered everything.