Celestial Lord has the "Hero" special rule which allows other units within 12" of the model to use the Celestial Lord's Quality (3+) for morale tests instead of their own. How is this useful? All of the other units have a quality of 3+.
With regards to upgrades the Celestial Lord can take "N" upgrades. The N section has "Replace Hand Weapon and Hammer:" which seems too imply that now the unit only has one weapon? Also, beneath that there is "Upgrade with any:" does that mean the unit can take any or all of the upgrades? Can the unit take "Upgrade with any:" upgrades if the unit takes the "Tempest Hammer" upgrade?
Last, and this is more of a general army management question, is there a template that I should write all of this down on? How do you keep track of what upgrades what unit has taken? Also, on the battlefield how do you keep track of which models are part of which units and which models have which upgrades? Seems like it could get confusing quickly.
The hero rule might matter if you have combined armies for example.
For the celestial lord that's correct, he can exchange his two weapons for one, and yes, he can take all upgrades (even on top of the tempest hammer).
It's totally up to you how you want to note down the units. Do it on a piece of paper, or digitally, or whatever else. To tell the units apart you can have them modeled with different gear, equipment or other details. Painting them differently also works pretty well.