You should upgrade or use an alternative browser. Vampiric Bite. Your fanged bite is a natural weapon, which counts as a simple melee weapon with which you are proficient.
Moonk Weapons: At 1st level, your practice of martial arts gives you mastery of combat styles that use unarmed strikes and monk weapons, which are shortswords and any simple melee weapons that don't have the two-handed or heavy property.
I read this as yes, so the Vampiric bite would scale as a Monk weapon and would use Dexterity instead of Constitution.
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That’s how I rule it in my campaign, actually have a Dhampir Monk right now too. I also rule that eldritch smite and divine smite works with the vampiric bite too.
Sure, it meets the requirements and, honestly, a vampire monk sounds like a pretty awesome combo. Shadow makes for almost a classic Bram Stoker's Dracula vampire, while Sun Soul would make for an interesting contrast/contradiction.
Only if you describe the technique as Fang Fu.
If this may be interesting for you, the "sun vampire" are in the list of races of "Tales of Arcana Race Guide", and you can get it in the 5e SRD (3PP section, of course) . 
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