#1 The Cid scene is likely much less confusing than people are making it out to be. Think a little less Western for a moment, first. Imagine a culture where "mind" and "soul" are seen as so intrinsically connected that "spirit" is a synonym for both; memory and soul are deeply entwined from this perspective.
The Warrior of Light's Echo resonates with his soul and helps give it strength and put it back in order. Typically the Echo is triggered by someone else having a strong memory; the Echo user is just brought along for the ride for that moment and they share a reverie. The Echo's target often experiences it as staring off into space and getting distracted before snapping out of it (though, rarely, a learned someone will notice you're in their head with them, like Raya-O-Senna once upon a time).
However, Cid didn't have the memories, either, until you put them back in order. It makes it even more likely he'd notice the effects of the Echo somehow. The scene begins with Cid asking Where did I get these goggles? and ends with You handing him his (metaphorical) goggles. His memories.
In all likelihood it's just a visual metaphor as Cid experienced it. Perhaps his third eye really did give him some kind of weird hallucination as you did it, but at the very least I'm fairly confident in the metaphor part.
#2 Recall that Ishgard's scriptures make reference to dragons being able to warp and control the minds of man? They present this as the origin of all heretics, and that's shown to likely not be true, but neither is it entirely a lie. King Thordan I himself was thrown into a ravine by a man overcome by Nidhogg's will. Estinien had a moment of weakness and doubt and the Eye seized on it. If I remember right, that was where the whole ruse started - Estinien's rage was being twisted into a desire to take revenge on Alberic for his part in Ferndale's destruction. Notice that Estinien even cries out with a desire to drink dragon's blood and gain the ability to tear at his enemies with fang and claw. He just lost the mental battle for a moment.
The Haldrath part is a little wonky. In English, Alberic speaks of Haldrath's armor being inside the crystal, as if you have Haldrath's old soul crystal, which would explain you evoking his memory and shade from it, if true, but it doesn't fully line up. German, for example, has Alberic suggest that your strength and charisma have unlocked some secret of the Celestial Dragons that only Haldrath previously understood, and that this evoked Haldrath's memory from Nidhogg's influence over Estinien. (That is the darkness spoken of; Nidhogg was aspected towards lower-case darkness.)
#3 Rhoswen is a Hyur and none of the other languages mention anything about it so I have no idea. Every language but English just says Carvallain's out on the terrace.
And yet to hear Eynzahr tell it, as soon as she was in real danger he swooped in and threw her over his chocobo "like a bloody knight of Ishgard", lol.
#4 I never knew quite what to make of that, either. Maybe, "I'm on break right now, but I wish I had the day off..." Is it weird that he's still on break? Sure. But that bookkeeper in Mor Dhona has been looking for that copy of Ona Ramuhda for like 4 years so...
#5 Doesn't sound like anything to me.
#6 In 1.0, these were Arcanist arms and were called "distaffs". They were recycled.