[RPG] Does ‘Aura of Hate’ also boost the damage of nearby hostile fiends and undead attacking you

Rules as written, no, auras don't require line of effect.

There is a general rule, regarding the area targeted by spells, on page 204 of the PHB:

A spell's effect expands in straight lines from the point of origin. If no unblocked straight line extends from the point of origin to a location within the area of effect, that location isn't included in the spell's area. To block one of these imaginary lines, an obstruction must provide total cover, as explained in chapter 9.

However, many auras are not spells - and even spells that cause auras do not have an "area" parameter described as an aura - there is no such thing. The target of these spells is typically a single creature or object that is invested with the aura, which is then described separately in the spell's description; the aura is not subject to the area rules which define who is targeted by a spell, and the creatures who may end up affected by an aura are not the spell's targets.

An "aura" seems to be an entirely separate concept which is not specially defined anywhere else. Thus there are no general rules describing how auras work and certainly no rule that states auras require line of effect, so the effect of an aura is only blocked by cover if the description of the aura states it is. Usually, the only criteria given is that the subject is within a certain distance of the aura's source, and there is no mention of any obstacles that might be between them - though there are many auras that specify that the subject must be able to see/look at the source of the aura as well, so line of sight is necessarily required in those cases.

The Antipathy (Sympathy) spell is a particularly unusual case which specifies an aura which takes effect if the creature is within 60ft of the source or can see it, giving it an astonishingly large effective range (and suggesting that line of sight is not at all required for the effect if you're within the 60ft radius).

DM discretion obviously applies.

Any given DM, of course, is free to rule differently. The spellcasting system establishes that line of effect is required as a general rule when targeting spells and affecting areas, so it's not wildly unreasonable to decide that other supernatural effects are subject to similar restrictions. Personally, if it came up, I would be tempted to houserule that the same rules that Detect X spells impose on their ability to detect "auras" apply to the propagation of other auras:

The spell can penetrate most barriers, but it is blocked by 1 foot of stone, 1 inch of common metal, a thin sheet of lead, or 3 feet of wood or dirt.

This makes for a more interesting tactical experience as regards positioning - wooden or shallow dirt walls would not usually offer any cover from an hostile aura or impede benefiting from a friendly one, but stone or metal walls would.

A) Do nothing - I am immune to this effect as a result of the aura.

From Crawford's Twitter:

RAW is unclear. RAI is that [the condtition] is precluded/suspended while you're in the aura.

Precluded: prevented from happening.

While Jeremy Crawford's Tweet was for Aura of Devotion, the wording on both Auras is identical save for the condition they affect, and the ruling should apply to both. My interpretation of the ruling is that:

1. If you are within your paladin ally's Aura of Courage radius, you are immune from being Frightened and do not have to save versus the Ancient Red Dragon's Frightful Presence.

2. If, at any point, you are outside the Aura of Courage radius and the Ancient Red Dragon used its Frightful Presence, you would have to save normally.

3. If you already suffer from the Frightened condition, then move within your paladin ally's Aura of Courage radius, the condition is suspended temporarily while you remain within the radius.

This fits both the RAW which states for Aura of Courage:

Starting at 10th level, you and friendly creatures within 10 feet of you can’t be frightened while you are conscious.

And also fits Crawford's Tweet.