Venturing into the desert, Cecil finds a village by an oasis.

Looking around, Cecil spots an inn and walks inside. The innkeeper is most accomodating.

The EasyType changes おだい (o-dai), a polite but fairly obscure term for price, to おかね (o-kane), the usual term for money.

Cecil walks inside and sets the girl on a bed. She looks up briefly, then turns away immediately.

The EasyType replaces Cecil's third line with the following:

Seeing that he's getting nowhere, Cecil lies down in a nearby bed and goes to sleep. The girl glances at him briefly before going to sleep herself. However, they're awakened when the door bursts open and a group of soldiers enter. Cecil rises to confront them.

Combat ensues. Being typical unmotivated grunts, the lesser Baron Soldier (Soldier) enemies only attack Cecil when specifically ordered to. The General (Officer) isn't any better; all he does is give orders, and if he has no one left to give orders to, he flees like a coward instead.

Darkness will end this battle swiftly, in two uses at most. If you would rather not use it or are playing the NA version, the soldiers should go down in a single attack each anyway, so it's not much longer that way. You can kill the General too, as long as you leave at least one soldier alive to keep him from fleeing while you beat him up. Doing so takes considerably more effort, particularly since the General is in the back row of the enemy formation (effectively doubling his defense and halving Cecil's hit rate), but it's also more rewarding (extra gil and exp). Not to mention silly; the Baron Soldier attack script makes them attack each other or themselves without the General to direct them.

In the DS remake, Darkness is again the method of choice for a quick win, except that with the changed mechanics, that means using the damage boost to obliterate the General. Taking him out leaves the others with Confusion status, and they don't seem to do anything once that happens.

She finally looks at him.

The DS remake introduces Whyt at this point, which I feel breaks the flow and ruins the mood of the scene. I'd have let it wait until morning.

They return to bed with no further interruptions. Rydia wakes first in the morning, and waits for Cecil to rise. They then leave the inn together.

Rydia may have a bit of a crush on Cecil at this point. Sure, he may have killed her mother, but that was sort of an abstract thing. He didn't literally take a sword to her. In contrast, he fought off former allies right in front of her to keep her safe, and no doubt looked really cool doing it. That sort of thing makes an impression.

Anyway, how about talking to some random townspeople?

By now, you should have a pretty good idea who the girl is. And, sure enough, Cecil walks into the back room of one house to find Rosa bedridden.

The old man nearby has a suggestion.

こうねつびょう (kounetsubyou) could also be yellow fever (黄熱病), but that's associated more with humid areas. I'm assuming it's 高熱病, which is simply a high fever, and Google supports this interpretation (when searching for 高熱病 with ローザ, I got 8590 results, versus 97 for 黄熱病 with ローザ).

Putting this together with what the other townspeople have said, Cecil concludes that he must head north to Damcyan and seek help from their royalty.

Be careful with Rydia in combat. She's not a fighter like Cecil, and she starts out at only level 1 on top of that. Make sure to keep her in the back row. She can defend, use items as needed, or use the Rod she comes equipped with as an item to inflict moderate damage, since her normal attack won't do much of anything. As she gains levels, she'll start learning magic. Try to conserve her MP until you need it, though.

The DS remake starts Rydia off with a few levels and spells already earned, so while she's still not a fighter, she's at least a bit less helpless.