1. What is the original body of the Emperor, Vitiate or Valkorian?

Vitiate.

2. Are both bodies active at the same time when both were alive? How is this possible?

Yeah, they appear to be. Presumably Valkorion has been building Zakuul for centuries, and definitely has been building the Sith Empire for centuries, so yes, he has been operating in two different bodies across the entire galaxy at roughly the same time.

How? I don't know.... something something force ...... power something something...

That said they did make a point of how Vitiate/Valkorion was "distant " and "distracted" (for instance Senya said he grew distant recently)... so that implies Vitiate can only focus mostly on one Empire at a time.... but he definitely is operating two bodies simultaneously, because otherwise "distant" and "distracted" would be replaced with "comatose" and "lifeless" as he was in the other body on the other side of the galaxy.

3. Assuming one was taken over by the other...how did these two souls meet? Opposite ends of the galaxy...

It's not two souls. Valkorion is just a name, body, and persona adopted by Vitiate for the Eternal Empire. Just like Vitiate possessed several bodies in the class stories and Ziost stories, Valkorion is just another host body for Vitiate as I understand it.

But yeah it's a good question how Vitiate is able to be nearly omnipresent across the entire galaxy... able to operate two Empires on opposite ends of the galaxy in secret all while manipulating countless scores of force users, fighting duels with powerful force users with the galaxy at stake, performing world devouring rituals, possessing whole armies and waging war on a galactic scale, while simultaneously romancing a human woman, impregnating her, and then raising children.

He's quite a complex fellow.... equal parts world devourer, galaxy conqueror, and family man.

4. Is the "true" physical body of Vit/Val placed in safe keeping...or does the soul become entirely incorpreal?

Well, the soul can be entirely incorporeal. Read here about the details of the power. That said, Vitiate's "true" physical body, his original, Sith pureblood body, is placed in safe keeping. Though I think it's probably just for sentimental (or somesuch) purposes.... I don't think Vitiate needs that body for any source of power or a source of his soul or anything.

5. Why does one embodiment behave like a gentleman and scholar and the other like a power-crazed madman?

Good question. Ask Bioware.

(The answer is likely because the power-crazed madman no longer suited the storyline Bioware wanted to put forth, so they just totally redesigned his character to fit their new goal.)