How I usually see this ruled:
1) The Darkness spell causes the area in which it is placed to be limited to Dim Light, as you spell out clearly. It is, however, not a [light] effect and furthermore does not add to the lighting level, rather setting the cap on illumination in the area to Dim Light. This is usually equivalent to creating a region of pitch-black magical darkness in the situations where the spell is likely to be cast, because the spell also prevents lower level spell-based magical lighting from working at all so there's usually no viable source of light functioning in the area of effect. Mundane light sources, however, are merely limited to not being able to raise the light level above dim. Most adventurers don't bother carrying any mundane light sources past about level 2, however.
2) No, you'd need a light source for that.
RAW, as I understand it:
1) Yep!
2) Yep!
It depends on where they are standing
The darkness spell is described in such a way as to give the impression that it is something tangible that spills out around corners, but can be blocked by objects. Think of darkness as not unlike a fog cloud spell.
The darkness spreads around corners. [...] Completely covering the source of the darkness with an opaque object, such as a bowl or a helm, blocks the darkness.
Likewise, darkness engulfs non-magical light - or rather, it cannot be illuminated by non-magical light. This means that magical light can illuminate it.
Light in 5e is described as having bounds. Faerie fire indicates that afflicted creatures shed dim light, which only means that area imposes disadvantage on Wisdom (Perception) checks; attacking into dim light behaves as normal.
This is where location comes into play. The bounds of the dim light must penetrate the bounds of the darkness spell in order to be seen. Put another way, there must be no darkness between you and the creature. You need to check the positions and radius of the area of darkness and creatures affected by the faerie fire.
If the radius of the darkness spell's area completely engulfs the radius of the dim light, they cannot be seen by you from any angle. If they are 5 feet or more away from the center of the darkness, they can be seen from the direction the dim light is from the center. This is sort of mathy, but really no more difficult than normal line of sight. Darkness spills out around corners continuously, so just visualize or draw the circles and draw a line to the center of the dim light.
Who do I have advantage against?
Advantage and disadvantage hinge on who can see whom. In general, you have disadvantage on attacks against targets you cannot see, and advantage on attacks against targets who can't see you. However, when neither target can see each other (such as when a target is standing in darkness and you are not), you have neither disadvantage or disadvantage.
From the basic rules on advantage:
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.
This means that faerie fire's advantage only has an effect when no disadvantage is imposed. It is important to note that, as explained in the question, faerie fire must be cast at a level greater than 2nd, or darkness will dispel it.
You have advantage against:
- Targets you can see that can't see you. It shouldn't matter the
circumstances in which this takes place (Devil's Sight, location,
etc); if you can determine who can see whom, this will suffice for
advantage.
- Targets affected by faerie fire that you can see
- Targets in any situation in which you have at least 1 source of
advantage and no sources of disadvantage
You have disadvantage against:
- Targets not affected by faerie fire that you can't see and that can
see you
- Targets in any situation in which you have at least 1 source of
disadvantage and no sources of advantage
You have neither advantage nor disadvantage against:
- Targets you can't see that also can't see you
- Targets affected by faerie fire that you can't see
- Targets standing in dim light that you have line of sight to (i.e.
you can both see each other)
- Targets in any situation in which you have any number of sources of
advantage and disadvantage (at least one of each)
This answer hinges on the fact that the darkness spell is dark in 3 dimensions, much like a 15-foot radius of fog or smoke. I believe this is true because of how the darkness spills around corners and can be blocked by objects.
If the darkness spell only "darkens" objects and ground in its radius, then it makes sense to imply that the faerie fire penetrates through it, making line of sight meaningless. Is it a floating black orb, or is it a radius of darkened objects? Again, I say the former, but I would personally leave this up to the DM.
Best Answer
Darkness (usually) cancels out all Advantage and Disadvantage effects for people affected
This is because of two basic rules that affect how combat resolves.
For the person outside the Darkness:
This is symmetric for the person inside the Darkness as well: they cannot see anyone they attack, and anyone they attack cannot see them either.
The semantics of these rules are found in the Unseen Attackers paragraph of the Making an Attack section of Chapter 9 of the Player's Handbook:
Since Advantage and Disadvantage cancel each other, and you don't consider stacked effects (i.e. 2 Advantage sources + 1 Disadvantage source doesn't result in net Advantage), Darkness almost always results in all advantage + disadvantage being negated for all affected creatures.
Shadow Sorcerers, Devil's Sight, and True Sight break this Symmetry
There are three features in 5th edition D&D that alter this situation.
In each of these situations, the Unseen Attackers rule comes into play, where the creatures that have at least one of these features will have advantage against any creatures that don't when attacking them, and said target creatures when attacking will have Disadvantage against their better-sighted assailants.
So what's the point?
Well, for starters, it does negate Advantage that your opponents might have. That's one good use.
Secondly, it makes it easy to Hide. Hideing requires some kind of cover, or some ability to stop the enemy from seeing you. So long as that dagger is out, the creature trying to evade the enemy can Hide as an action whenever they want, and if their Dexterity(Stealth) roll is high enough, their location becomes unknown to their enemy (though known to be somewhere inside the Darkness bubble), which will make it much harder to hit them, even without Disadvantage on their attack rolls.
Resolving the unknown location, mechanically, is DM fiat; generally, the DM makes creatures target random points within the bubble, and if they're more than 5' from the creature, they're not close enough to hit them. Otherwise, they use their Action to use the Search action, and if they roll high enough, they're able to know the location of their target
Another important use of Darkness is to prevent spellcasting that requires visible targets. The vast majority of spells, especially single-target spells, require visibility of the target in question; obscuring vision with Darkness makes such spells unusable.