Question is rather straight forward. There are three specs one can use while playing a rogue. I'd like to know which spec will make leveling the easiest vs which one should I switch to in the open world in the event of PvP.
For PvP, Subtlety is the current king of specs. For Shadowstep, Shadow Dance, Preparation, Premeditation (Gets combo points to get Recuperate rolling after a Vanish), massive Ambush damage, and faster Stealth movement. All three are decent for PvE leveling, with combat being the best for multiple enemy encounters. There really isn't a "wrong" spec for leveling. If you are on a PvP server and want to have the best PvP abilities all the time, I would level Subtlety spec.
To answer specific questions: If you're in a PVE spec and are engaged in PVP, you have 2 choices, stay and fight or vanish and switch specs (may not be possible).
(ON a PVP server) IMO a rogue should ALWAYS be in PVP gear while leveling, the differences in damage is minor while solo leveling. If you're in a party or group then put on PVE gear. If you do a dungeon or Raid put on PVE gear, if you're on a PVE server and are solo leveling and not flagged for PVP use PVE gear.
As to which spec is easiest to level with, well that is completely depended on your play style so I can't answer that directly, below I wrote up some of the differences between the specs.
I leveled the full way with subtlety, and I've pvp'd and pve'd (including end game raiding) with subtlety. I had 2 subtlety specs one for pvp one for pve, they had slight changes but those changes are very needed to increase your damage for pve.
Subtlety is heavily focused on being stealthed, then attacking and doing (big) damage, then re-stealthing as soon as you can. It's great for leveling because of the burst damage, it'll knock more then half the health off of most mobs so by the time they can hit you they'll be about dead. Subtlety is great single target dps.
Not getting hit is key to staying alive, as subtlety try to ALWAYS be behind the enemy, only times to be in front is if the enemy has you targeted (you can't get behind it), or if you're in a RAID and your raid requires you to stand with your party for AOE heals.
In PVP always try to re-stealth as soon as you can, stealth is your friend and part of you, try to use it all the time.
Assassination focuses on poison damage and finishing moves. It too is a single target dps spec and does very well at it. The Assassin does it's first attacks from stealth (not as high burst damanage as subtlety) then finishes it's enemies off without re-stealthing.
If attacking multiple targets, try to keep your poison dripping on a few enemies (not all of them) as it'll decrease the time in a fight while still focusing a single target mostly. Also in PVP a dot (poison) will prevent others from re-stealthing (for to long).
Assassination is much tougher then Subtlety (but not as much as Combat), can take more hits and doesn't have to move as much.
Combat is more of a (swashbuckler) in terms of how it fights, stealth is used more as an afterthought and not a primary focus.
You're tough and can take the hits and dish it out, you are made to fight multiple enemies and do decent damage over all while still doing pretty good single target dps.
Combat used to be the top PVE build for raiding as it could dish out the most damage, but last time I was playing the patches had brought the other classes up to spec.
Combat can be used in PVP but because your damage isn't stealth depended it doesn't make as much sense to put points into stealth skills, so most combat rogues only stealth at first then stay out in the open after (unless no ones around).