[RPG] How does a Cloak of Displacement interact with surprise or hidden attacks

Coming Out From Behind The Wall

Maybe. Here's the thing. If the Rogue has to come into the open to do this, he's no longer hiding (you can't hide in the open). No spot check is needed to see the Rogue if he just walks out into clear sight of the Ogre, he's no longer hidden. As he's no longer hidden, he'll need some other condition to allow for a Sneak Attack (flanking for example).

This is one of the reasons why Hide In Plain Sight is so good. If you had that, the Rogue could attempt to remain hidden even out in the open and this would work. Shadowdancers for example can stay hidden if they're near a shadow. That would include the shadow of the wall or the Ogre itself, making it a LOT easier to attack while hidden.

Rules Compendium Changes

The Rules Compendium (page 92) adds some extra things to Hide, if you're using it. Those address coming out from hiding a bit differently. In this case the answer would be Yes, if you can make the new Hide check as detailed below.

Move between Cover: If you’re already hiding thanks to cover or concealment, and you have at least 5 ranks in Hide, you can make a Hide check (with a penalty) to try to move across an area that doesn’t offer cover or concealment without revealing yourself. For every 5 ranks in Hide you possess, you can move up to 5 feet between one hiding place and another. For every 5 feet of open space you must cross between hiding places, you take a –5 penalty on your Hide check. Movement speed penalizes the check as normal.

Sneak up from Hiding: You can sneak up on someone after emerging from a hiding place. For every 5 feet of open space between you and the target, you take a –5 penalty on your Hide check. If your Hide check succeeds, your target doesn’t notice you until you attack or perform some other attention-grabbing action. Such a target is treated as being flat-footed with respect to you.

Sniper

Yes. It's specifically mentioned in the Hide skill:

If you’ve already successfully hidden at least 10 feet from your target, you can make one ranged attack, then immediately hide again. You take a -20 penalty on your Hide check to conceal yourself after the shot.

Being aware of someone isn't enough to prevent Sneak Attack. If the spot checks fail against the new hide check, then the Rogue is hidden again and can continue to sneak attack.

Hiding and Sneak Attack

Yes, being hidden with Hide makes you effectively invisible, which normally allows Sneak Attack. Again from the Rules Compendium (p. 92):

If you’re successfully hidden with respect to another creature, that creature is flat-footed with respect to you. That creature treats you as if you were invisible (see page 76).

Yes, advantage would negate disadvantage for purposes of Sneak Attack.

According to the rules on advantage and disadvantage (PHB 173, emphasis mine):

If circumstances cause a roll to have both advantage and disadvantage, you are considered to have neither of them, and you roll one d20. This is true even if multiple circumstances impose disadvantage and only one grants advantage or vice versa. In such a situation, you have neither advantage nor disadvantage.

So, for example, if you (the rogue) have both advantage and disadvantage on an attack roll against an enemy while your ally is within 5 feet of the target, you could make a Sneak Attack because you are treated as if you don't have disadvantage when making the roll. This complies with the requirements for Sneak Attack (PHB 96, emphasis mine):

Once per turn, you can deal [extra] damage to one creature you hit with an attack if you have advantage on the attack roll.... You don't need advantage on the attack roll if another enemy of the target is within 5 feet of it, that enemy isn't incapacitated, and you don't have disadvantage on the attack roll.

However, if the ally were absent in that situation, you could not make a Sneak Attack because you are treated as if you don't have advantage when making the roll.

The same rationale would apply for features other than Sneak Attack that depend on either advantage or disadvantage on any attack roll, ability check, or saving throw. When any such roll is made with both advantage and disadvantage, the roll is made as if it actually has neither advantage nor disadvantage. In this case, no feature which requires advantage or disadvantage would be activated, and no feature which forbids advantage or disadvantage would be precluded.