I like the concept and the abilities are very flavorful. However, there are a few things that need a little bit of work. Mostly, you need to specify what it takes to activate a power (reaction, bonus action, etc...) the duration of the effects, and whether or not they require concentration (I'll give you example).
I also suggest you to make this a prestige class modeled after a Oath: So you need to set up a minimum--say--Dex and Cha score to have, and a task that these knights need to accomplish to have access to the order. That said, I suggest you to provide the "Divine Smite" (and Improved Divine Smite at level 11th) feature to this class, the extra attack at level 5th, various auras and ASIs as per the normal paladin class. Except Aura of Protection, I'd suggest you to roll that into the Moonbrand. Now, onto the rest.Moonbrand
I'd suggest you to have it use a bonus action or reaction to activate and make it usable only a limited number of times per short rest.
Example: Once per short rest at (twice at level 9 and thrice at level 18), as a bonus action, you can manifest it as Eilistraee's moonfire to bless both your weapon and your allies'. It grants you and your allies within 10ft (20ft at level 9th; 30ft at level 18th) the following effects:
-You and your allies are surrounded by a swirling orb of moonlight that can dispel magical darkness and be moved and directed by you (40ft per round). As an action, you can consume the orb to direct it at a hostile creature, dealing 1-2-3-4d8 damage (as per cantrip progression). The orb will be returned to you in the next round (this is the iconic canon Moonfire effect).
-You and your allies gain advantage to all saving throws, and enemy attacks agaist you (but you only) are rolled at disadvantage (stand in for aura of protection).
-You and your allies gain advantage on attack rolls, and your attacks deal an extra 1d8 damage. The advantage is also applied to the Moonfire attack, and the extra 1d8 is also added to the Moonfire damage (basically taking it up to 2-3-4-5d8). This stacks with Divine Smite.
This effect can be used as a reaction when you or your allies must take a saving throw. You need to concentrate to maintain this effect, and can do so for a maximum number of rounds equal to your CHA modifier.
Sounds good to me. Just make both effects require a reaction to apply the malus to the enemy. Maybe make the effects usable only up to CHA times per short rest if it is too powerful
-----------------------------Harbinger of the Dark Dancer
I'd suggest to make it last CHA rounds, up to 5 (after the first), and to make it usable only once per long rest. IMO it should be activated as an action, like others level 20 paladin features.
I like the passive, but I think that it'd be cooler if--instead of providing that passive--summoning this effect applied Moonbrand within 30ft from you, with the only difference that you'd get advantage on saving throws as normal, but you (and only you) would also basically get old 3e D&D improved evasion against enemies of faith (maybe you enter a battledance becoming more deadly and elusive at the same time). Leave the damage reflection out IMO, because between arrows and spell turning this class already has a lot of it.
I personally think you should make the 3 possible attacks usable against anyone, otherwise this class won't be very appealing in most campaigns.
-Magic Missiles must take an action IMO, but it's fine. It would replace the bolt of moonlight that Moonbrand provides for your character. Its damage should be somthing like 1d4+2 per missile (9d4+18 total), or 1d6+1 per missile (9d6+9 total)
-Turning spells needs to take a successful reaction and opposed test to succeed, otherwise it'll be very powerful. For example, proficiency+CHA vs enemy proficiency+enemy casting stat; with advantage when the test is made against enemies of faith--mainly yochlols, demons, priestesses of Lolth, or the likes. I wouldn't have it work on a normal evil drow, because your goal should to open their eyes and hearts, not slaughter them. Make it turn up to 5th level spells against non enemies of faiths, and any level against enemies of faith.
ALTERNATIVELY, instead of turning spells you could maybe use a streamlined effect. For example, if you succeed the opposed check, the spell is denied and the attacker is enveloped in silvery flames that deal 1d8 (radiant or cold) damage per spell level reflected. Furthermore, the flames linger, dealing 1d8 damage each round for each 3 levels of spell deflected, revealing the target, and making every attack against it deal 1d8 extra damage for each 3 levels of spell deflected (lasts until a successful Will save with DC equal to 8+your proficiency+you CHA modifier). If the spell applies a condition, then the attacker is also incapacitated for 1 round. For example, deflecting a "finger of death" would nullify the spell and envelop the necromancer ins silvery fire that deals 7d8 damage, plus 2d8 each round. Each attack against the necromancer would also deal extra 2d8 until it makes a will saving throw.
But spell turning belongs to the original Sword Dancer class, so I guess it fits better than this.
-About the weapons, in 5e +5 swords don't exist. The upper limit is +3. IMO, this feature should provide an alchemical silver Holy Avenger, or 2 +1 alchemical silver frostbrands