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.
No, Maddening Darkness has a fixed position
This is a case of Specific vs General
The general rule is that when you cast a spell, its area of effect is fixed. Once you select its point of origin, it stays there.
Typically, a point of origin is a point in space, but some spells have an area whose origin is a creature or an object.
This clearly indicates that, unless a spell explicitly says otherwise, a "point you choose within range" is a point in space. This is seen in spells like Fog Cloud, Create Bonfire, etc.
Some spells, such as Darkness, Anti-magic zone, Aura of Life, etc. invoke the exception to make the point of origin an object or creature that can move, taking the spell with it. Every such spell explicitly states what the target can be and that the spell "moves with [you/it]."
If Maddening Darkness could be relocated by aiming it at an object, and then moving that object, the spell would explicitly say so. Without a specific override, Maddening Darkness is subject to the general rule that your target is a 'point in space.'
Best Answer
For most spells, no.
As described in the "Areas of Effect" section of the spellcasting rules:
This point of origin is a point in the space from which the magical energy spreads, but it is not its source.
The description of Antimagic Field says, in part (bold for emphasis mine):
Hence, if a Fog Cloud is hovering somewhere and an Antimagic Field is cast nearby intersecting the area of effect of the former spell, then the fog is suppressed only in the intersection of the two areas of effect, even if the point of origin is included in this intersection.
For some spells, yes.
There are anyway some spells for which covering the object which is the origin of the spell suppresses the effects on the entire area of effect. For example, consider the Darkness spell that you mentioned (emphasis mine):
Hence, if Darkness is cast on an object and the Antimagic Field includes that object, the darkness produced by the spell disappears. Indeed, the description clearly states that the origin of the darkness is the object: blocking the magic coming out of the object via an Antimagic Field blocks the effects of the spell.
This suppression is confirmed by another part of the description of the Antimagic Field spell:
On the other hand, if Darkness is cast choosing a point in space as origin and the Antimagic Field includes such point in its AoE, then the Darkness is supressed (i.e., there is no heavily obscured area caused by the spell) only in the intersection of the two areas.
The same happens for the Light cantrip: