How definitional is sneak attack to the rogue? Should it be an option or an inherent part of the class?
I wouldn't call it "definitional" so much as "the easiest way to explain how a rogue can take part in combat." A fighter's combat contribution is obvious. Wizards have a fearsome array of combat spells, and clerics can heal and buff their friends. Next to all that firepower, what does a small, sneaky person with no magic have to offer? Unless you subscribe to the theory that it's okay to have a non-combatant class in a combat-heavy game like D&D, sneak attack or something like it is the obvious answer.
I would not object to seeing the sneak attack become one trick among many, however.
How should sneak attack work?
The way it works now is okay, but I'd like to see more emphasis on the stealth aspect. In 3E and 4E, rogue stealth goes out the window once a fight begins; it's all about flanking. If rogues had some kind of ability to avoid notice in a battle and "charge up" their sneak attack, then strike for a ton of damage, that would make it feel more sneaky. At least to me.
Should a rogue emphasize a surprise attack? Combat positioning (flanking)? Both?
As my previous answer indicates, I favor surprise attack over flanking.
How should a rogue's social skills be implemented?
That's a tough one. Gonna have to ponder that.
How should a rogue's perceptive skills and trap/lock expertise be implemented?
I think 4E handles this pretty well.
What mechanics does a rogue need for self-defense?
Stealth and evasion techniques. IMO, rogue AC should be crap and their hit points mediocre, but if you take your eye off one for so much as an instant, poof! She's gone. Until a couple rounds later when you find her knife in your back.
What, in the broadest D&D sense, is a rogue?
In a dungeon crawl, the rogue is a stealth and infiltration specialist. Hence why I want to see their combat abilities designed around that model. In a more general sense, the rogue is the one who always has a trick up her sleeve. Locked door? Out come the picks. Being chased by a monster? Improvise a trap. Need a place to lie low for a few days? The rogue knows a man who knows a man.
(This "always have a trick ready" role has traditionally been filled by the wizard. I would like to see the wizard surrender some of that turf--not all of it, mind you, but some--to the rogue, and focus more on countering arcane threats.)