There are a few problems here
First: you can't attack with two-handed weapons and get the dueling bonus
Does Dueling Preclude Use of Two-Handed Weapons? - check here if you have doubts.
Second:
Sacred Weapon: As an action, you can imbue one weapon that you are holding with positive energy, using your Channel Divinity. For 1 minute, you add your Charisma modifier to Attack rolls made with that weapon
This bonus is added to the attack roll, not to the damage roll. I.e., it increases your chance to hit, not your damage.
Also, note that it takes one action to get the buff, thus he can't attack in the same turn he used this feature.
Therefore, the actual damage on hit would be either
- 1d10 + 2 + 2d8 using the versatile property of the longsword
- or 1d8 + 2 + 2 + 2d8 attacking with only one hand of the longsword.
Yes, if the racial rule calls them weapons
(This answer has been updated to reflect the apparent shift in the wording of the rules since Explorer's Guide to Wildemount. The original answer is below the horizontal rule.)
User Mavoc points out that the wording for most of the races with natural weapons has been revised. The online version of those races (and printed versions since Explorer's Guide to Wildemount) uses slightly different wording from previous publishings:
Your talons are natural weapons, which you can use to make unarmed strikes.
Further, it seems this wording change "which you can use to make unarmed strikes" has ben retroactively applied to virtually all races that have natural weapons on D&D Beyond.
For context, the PHB (page 119) states:
Instead of using a weapon to make a melee weapon attack, you can use an unarmed strike: a punch, kick, head-butt, or similar forceful blow (none of which count as weapons).
So, while general rule that unarmed strikes can't work with Improved Divine Smite because unarmed strikes aren't weapons, the rule for races like the Aarakocra, specifically says that the relevant anatomy is a natural weapon. This would allow it to work with abilities that require a weapon despite the fact that an unarmed strike is being made.
As your other linked answer states, Unarmed Strikes do not work for Improved Divine Strike because the rules say Unarmed Strikes are not weapons:
Instead of using a weapon to make a melee weapon attack, you can use an unarmed strike: a punch, kick, head-butt, or similar forceful blow (none of which count as weapons).
But the racial ability for Minotaur horns specifically says the horns are a weapon:
Your horns are natural melee weapons
What is happening here is that there is a specific rule/allowance for the Minotaur that is similar to (but different from) a general prohibition.
The minotaur is not making an Unarmed Strike (a head-butt). It is making an attack with a weapon which happens to be located on its head.
Contrast this with the Aarakocra's Talons:
Talons
You are proficient with your unarmed strikes, which deal 1d4 slashing damage on a hit.
(Hat tip to Justin for the Aarakocra example)
Also, Jeremy Crawford has tweeted an affirmation of this answer.
Best Answer
Sure, once per day, if they roll max on everything
This works. But there are some caveats:
If your adventuring day consists of exactly one enemy, this is a great idea. If it does not, they had better hope that the rest of the enemies they face are having an off-day because they've just blown basically everything they had on a single strike.
D&D 5e allows for a lot of crazy broken stuff if you allow your characters to rest after every encounter, because it allows certain classes to just blow their entire load of spells and abilities on a single encounter and then rest. But the adventuring day should have more encounters than just one, or the balance system breaks down, the DM manual does a pretty good job at explaining this principle.