Cecil and Cain must pass through this cave on their way to Mist Village. As the name suggests, a thick mist covers the cave.

The monsters are insignificant next to the party's combat prowess, but every so often, a mysterious voice is heard...

Near the far exit, the voice delivers an ultimatum.

As Legends of Localization notes, rewriting this question makes sense since Japanese はい and いいえ function more like "agree" and "disagree", particularly in response to negative questions, than like English "yes" and "no". The original question, at its most literal, asserts that they have no intention of, or no interest in, turning back, and asks for confirmation. Responding "yes" to a question like that, while it could be taken as "yes, I won't turn back, just like you said", usually means "yes, I will turn back after all" instead. Japanese はい is unambiguously "you are correct in saying that I will not turn back". For clear communication in English, it's safest to avoid that sort of negative question altogether, and if you're asked one, to avoid simple "yes" or "no" answers.

The English DS remake does something similar, making the quesiton about whether they choose to disregard these warnings.

The mist becomes a Mist Dragon, and the first boss battle ensues.

This is a bit of a puzzle boss, though not much of one. Just don't attack when the dragon turns to mist...

...since it has no effect, and the mist will strike back. The in-battle dialog says as much if you attack anyway:

After a delay...

This should be trivial unless you're careless.

The Mist Dragon has no weaknesses and absorbs Holy (not that it matters). It changes forms every fourth turn, attacking for three turns when solid and taking no action, except to counterattack with Chilling Mist if attacked, for three turns when mist.

The DS remake leaves this battle mostly unchanged, except for giving the dragon a weakness against Dark for Cecil to take advantage of.

A few steps after they enter the village...

And a small horde of Bombs fly out and set the village on fire...

Cecil turns toward the source of the crying sound.

The moved line in the NA version has Cecil turning before he hears anything. Huh? Without anything to break the text apart, I suppose it would look like he were the one crying out otherwise, but still.

Cecil walks toward the sound, and Cain follows. They find a young green-haired girl in a blue dress crying over a woman who appears to be dead.

The girl backs away.

Cecil looks upset...

But I think the NA text really fails to convey how horrified he is. It's bad enough that the town's on fire thanks to him, but this? Cain, on the other hand, seems fairly calm, though it's unclear whether that's because he's more callous than Cecil or because he's better at controlling his reactions.

The EasyType replaces こんな　さつりく (konna satsuriku, such slaughter) with こんなこと (konna koto, such a thing), adding euphemism and avoiding an uncommon term.

Cecil gets in Cain's face.

The EasyType changes two of Cain's potentially confusing words to simpler and more straightforward alternatives: いきがる (ikigaru, to put on airs or act bold) becomes はむかう (hamukau, to rise up against), and えんご (engo, backing) becomes たすけ (tasuke, assistance).

Cain glances to the side before turning back to Cecil and changing the subject.

They walk over to the girl.

Honestly, what was he expecting? They just killed her mom and set her village on fire, so now she'll just trust and listen to them? Not a chance.

The girl backs away. Cain pushes Cecil aside and advances on her.

Ah, Cain. Master of tact and diplomacy.

The girl backs away several more steps.

Cain and Cecil approach her again. Predicably, she doesn't take this well.

In my opinion, the DS remake, while it goes a bit overboard with Cecil's screaming-WHY-at-the-sky initial reaction, handles the rest of this scene masterfully. The grief-stricken girl mostly just sits there until she's had some time to work through it, Cecil plainly emotes his devestation as he realizes what he's done, a wary Cain overplays the part of a heartless soldier to maneuver Cecil into being the first one to suggest defying orders, then the two of them get so caught up in their discussion that they completely forget about the girl until they make up their minds to leave the area, at which point they're in such a rush that they drive her into a panic, and, best of all, the girl, upon realizing that fleeing isn't going to get her anywhere, lets her fury explode into a rage-summoning that she can't control rather than let them have her. It's every bit as emotionally-charged and dramatic as it ought to be.

Out of curiosity, I tried looking for a Japanese-language version of the scene on YouTube, and found one from the mobile version (which is a port of the DS version). Cecil's screaming at the sky is far more subdued, though I also felt that some later parts of the scene, which should have been more heated, seemed overly calm. As for another thing I'd been wondering about, I also noticed that the Japanese text is almost entirely identical to the original SFC version of the game. The only part that seemed to be changed at all was Cecil's line about bringing the girl with them. The original line almost feels like "I guess we can bring her along, if we really have to." It was revised to something more like "Of course we'll bring her with us!" It might be interesting to scrutinize a full playthrough for that sort of thing...

A battle against the girl begins. She's not happy.

She also has 60,000 hit points in this battle. Must be eating her Wheaties.

She Summons a Titan, which then damages Cecil and Cain with an with an earthquake. More problematically, the quake gets so out of control that it rearranges the surrounding terrain. Cecil regains consciousness later to find the girl lying nearby. Cain, however, is nowhere to be found.

Cecil takes the girl with him as he leaves the area. An apparent rockslide blocks the way between Mist Village and the location where he woke up, so he has little choice but to continue east, where the valley leads to a desert.