[RPG] How is the celestial template applied to a paladin’s mount

In all cases the answer is of the druid, because those attributes (Cha, HD) are not altered by wild shape. I think you may be missing the profoundly different way polymorphs work in Pathfinder.

The druid's wild shape ability works like the beast shape spell. And the beast shape spell is a polymorph effect. Read polymorph carefully.

While these spells make you appear to be the creature, granting you a +20 bonus on Disguise skill checks, they do not grant you all of the abilities and powers of the creature.

You do not get the creature's HD or Charisma at all. You get physical attribute bonuses and natural armor based on size, get the creature's movement type and natural attacks (based on your BAB and STR), and specifically listed abilities. This is a significant departure from other editions. You barely need the original creature's stats at all to wild shape - you need its size, number and type of attacks, movement type, and some special abilites (trip, rake, blindsight, etc.) and that is it.

I don't know that "ordering" is the right way of thinking about it - when you turn into the animal, your HD is your HD, not the animal's HD. Whether you think about it as "order" or think about it as "the animal's HD just changed to mine," in either case you'd use your druid's attributes on the lookup table and calculations.

You get the SR and Smite Evil because you change to the animal form and then "apply the template to your animal form" as the feat states.

As written, yes, they are different

More than likely, this is just an oversight (and if not, poor choice to call it Smite Evil if it isn’t actually Smite Evil!), but as written a Celestial creature’s ability to Smite Evil is not the same as a paladin’s.

Actually, as written, the ability is very strange! It says that you add +Cha to attack and +HD to damage against evil foes. Not a single, chosen evil foe as with the paladin, but to any and all evil foes, apparently. But then it says that it lasts until the target is dead, even though it did not previously say anything about targeting anyone. What that even means, I can’t say for sure; is it the first evil foe slain by the Celestial creature after activating the ability? Or does the Celestial creature just pick some “target,” the only relevance of which is that the ability lasts until that target dies? Doesn’t even say it has to be an evil creature, or an enemy for that matter; “target” your ally, and provided you don’t let him die, get +Cha to attack and +HD to damage against all evil foes until the next time you rest?

More than likely, they meant that you only get +Cha to attack and +HD to damage against one specific evil target of your choice, rather than against all evil foes, but that’s not at all what it actually says. Moreover, that still makes very little sense, as it’s called Smite Evil so it should work like Smite Evil. I think it makes vastly more sense to just use the paladin’s version and be done with this silliness.