1) Why is there a separate world to role play apart from the survival-faction worlds?

Speaking as a member of lore staff, it's much easier to moderate lore and conflicts that happen when there's a place specifically for roleplay. The game rules in the roleplay world are different from survival rules. Lore staff usually aren't interested in upholding survival rules (plus game staff are all trained and most lore staff aren't trained to handle game matters), but we're very passionate about the roleplay world and will often gladly step in to resolve conflicts.

As a roleplayer, I feel much safer in a separate world with no PvP. Usually PvP is disruptive to a scene. Imagine a dramatic plot is going, something that's got you at the edge of your seat, and the story is interrupted when someone comes and kills the group. I don't feel entirely safe roleplaying in the survival worlds and for me to be able to really enjoy the game, I stick to regalia.

I've also had this happen a number of times throughout the past few years. The group I usually stick with used to predominantly roleplay in survival worlds and once they started becoming more active in the community, they got raided more. When we created a new faction that encouraged survival world roleplay, we were also often raided. It's a clash of interests. People who are presently roleplaying don't want to pvp, and pvpers don't want to roleplay out a combat scene.

As for why Minecraft, personally I like having settings and characters to move around. Forum roleplay is fun, but can be arduous getting worked up describing scenes and appearances. It also ensures consistency. If someone set a flower pot on the table, no ones going to forget about it because it's right there.

 How do you determine who gets authority in role play?

It's usually on a trust or sign up basis. Tons of info on that on the roleplay sections of the forums.

We like having authorities to be able to mitigate disruptive and blatant crime. Someone comes in to shoot up the tavern -- how often does that happen in real life? What if they stab somebody, or a bunch of people?

Guards are about to ensure the maximum amount of fun for the maximum amount of people. They're also there to ensure those roleplaying as criminals exercise a little caution. Often, scenes like that are superficial and detrimental. Being stabbed for no reason is much less interesting than being stabbed by an ex lover who's been stalking you for seeks.

There used to be a trope where people would run into the tavern, proclaim how much of a vampire they were, and proceed to recruit or attack people in the street. People didn't enjoy this. It was disruptive and often shattered immersion. People would get in ooc arguments and eventually someone had to step in. It wasn't satisfying to be randomly jumped on the street -- it's the plots leading up to it that are typically the most satisfying.

That doesn't happen nearly as much as it used to. The guards are part of the reason for that.

3) Why, generally, do role players dislike pvp?

I don't like it, personally, because it doesn't interest me a ton. I started playing Minecraft as a builder, dabbled very briefly in PvP, got super interested in plugins, then I found roleplay and took a strong liking to it. PvP just isn't my thing. I stayed on massive for the roleplay.

My big question to you is, what are you trying to gain out of this? The way you phrase the expansion on your questions is a bit strange. It suggests you already have very strong feelings on your questions. I'd love to pick your brains.