He doesn't. 

He is worried that Ira doesn't like him, but tries not to show it. 

Going from where she looks, facial micro-expressions, and postural body language (assuming that Kiritsugu's experience translates, anyway), she seems like she might be conflicted about something that he reminds her of, which could contribute to an air of dislike.

It has only be about 24 hours since he showed up, though. Social dynamics are complicated, who knows where it will go.

After supper, Thia will head back to the green room, bringing the rocking chair and one of the family's small collection of books to sit and read, while Bran and Ira head upstairs to work on dolls.

Once they're upstairs, he asks in a hushed voice: "Have there been other travelers like me? Ones who... didn't make it?" 

Ira only redoubles her focus on carving fine details into the dolls faces and fitting them with little doll-sized clothes, while Bran turns to answer Kiritsugu. "Only one, at after my mother's arrival here. Ira's mother, Minessa, came here about thirty years ago, and gave birth to Ira a few months after that. She was with us for a little over three years. That summer, she went out to gather eggs from the coop, and the cave-sleeper was stalking just beyond the berm between it and the woods proper. It attacked her, and though I managed to wrestle it off her body, she did not survive."

"Oh," Kiritsugu says. "I am sorry." 

What a pointless death. He is glad he has sided with this family against the beast.

Everyone continues their work with the dolls in silence for a while before Ira speaks up. "We usually talk about what we imagine the dolls' lives are like, what sort of world they live in. I like to at least, and Bran plays along. Would you mind if we did that?" She looks to Bran, then back to Kiritsugu. "You could join in, if you want?"

He smiles at her. It looks less pained than his first few smiles. "I'd like that." 

He points to a doll at random. "What about this one?"

Ira smiles back with a mixture of apprehension and gladness. "That's Mahuk Na..." She places a finger on her chin as she attempts to remember, or perhaps is pondering for the first time. "Ah, Mahuk Na Aknenhy! She's a bug-tamer who works with giant beetles..."

She will proceed to describe the life of this character, evidently a relatively important person in the world that Ira has built, in great detail, happily answering any questions about her life or world that Kiritsugu asks, and even pointing out some other dolls from the same world, some of whose stories intersect with Mahuk's directly while others only happen to exist in the same broad world but situated far apart from her whether in space or time.

Bran is smiling all the while as well, evidently happy to see his niece getting along with Kiritsugu.

Kiritsugu is genuinely fascinated. 

He'll keep asking questions, even suggesting the occasional element, until he's tired, and maybe even after. 

He's also missing his daughter with crushing violence, but there's nothing he can do about that. 

Ira is absolutely and totally absorbed in talking about this, and is plenty happy to incorporate Kiritsugu's proposals and explore their implications.

Bran can detect that there's something troubling his new friend, and after Ira has gotten tired and gone off to bed but before he and Kiritsugu do the same, he'll ask, "Are you alright, my friend? Is something wrong?"

Something about Bran makes him honest. 

"I... had a daughter." He says. "I threw her away for reasons that meant everything to me at the time and now mean nothing. Your niece reminds me of her, or perhaps of what she might have become." 

Bran nods grimly. “I’m sorry you have to carry that burden. If you have some memento of her and are still here for Wishing Night in a few months, perhaps you could wish to see her again? I don’t know if the hearth is powerful enough to reach across worlds, but it may be worth a try?”

"I'll think about it," he says. 

He's not sure he does. He also doesn't want yet another apparition of his daughter, created only to taunt him.

Bran will nod again in understanding, and will leave the topic alone until Kiritsugu decides to bring it up again. Bran then heads to bed. Presumably so does Kiritsugu, unless he decides to stay up and check anything around the cabin or perhaps even outside on his own?

He's been assured the cave-sleeper will be asleep, so it is now time to explore.

Well, he calls it "doing reconnaissance."

Kiritsugu is already familiar with the inside of the house (aside from possibly the shower room, nestled between the two bedrooms upstairs). Outside, he can find the chicken coop that was visible from the green room, as well as the earthen berm that separates it from the woods.

The world here is eerily quiet, only the sounds of small insects and the rustling of warm summer wind. The stars swim in the night sky in a way that might give Kiritsugu vertigo, like he's looking down on some great pool of dark water. In the wood it is exceedingly dark, the starlight blocked by surprisingly thick cover of pine-needles. He migh encounter one or two clearings where small bushes and shoots grow, similar to ones he saw along the outer edge of the woods on the walk to the cave and back, some of which he may thus recognize as edible, though here they're mixed up with unfamiliar or clearly poisonous ones.

Venturing away from the woods, he'll only find endless stretches of grass waving gently in the wind, and maybe a small pond or stream if he travels until he can only just barely make out the cabin through the darkness. It's hard to tell exactly, but it feels like there's a slight grade downwards away from the woods, as if it's at the top of a hill with a very gentle slope.

He's going to go and bother the chickens. He's curious about the fact that they're almost on a hill, but that seems like the sort of thing to deal with in daylight. He's terrified of getting lost out in the woods, and not finding his way back.

The chickens are asleep at the moment,  though if he enters the coop and prods them a bit he could wake them up, which would evoke some irritated squawks and maybe some pecking.

He's not going to do that, he's going to look at them admiringly. 

This place is so strange. The life here is so familiar, but clearly he is no longer on Earth. 

Are there ways he can explore without getting lost?

If he focuses on his magical senses and maybe turns around in a circle, he can feel the direction that the hearth's gentle, warm magical vibrations are coming from, even if it's entirely out of sight, which seems to serve as a passable compass.

Oh, that is useful. 

He strikes out into the woods, too excited by this revelation to think about bringing water, and tries to see whether the incline of the land changes. 

The land within the woods is pretty level, though there is the occasional noticeable bump or divot. Nothing on the scale of the broader downwards incline away from the trees.

If he wants to try and get a good view of the entire area, he could try climbing up a tree? Here is a particularly tall and sturdy one.

He climbs the tree, feeling like a little boy.

This tree is one of the oldest in the whole wood. It's from an older generation, one of the few survivors of a fire that burned down most of woods here. Somehow, it carries a sense of grief, but also perseverance.

From the highest branches that Kiritsugu feels comfortable putting his weight on, he can see the whole woods, including the cabin and the cave on opposite ends, and a long ways beyond. It definitely seems like the woods are at the top of an incredibly large and but very gently sloped hill. Strangely, there seems to be an element of uncertainty or dreamlikeness to the furthest reaches of this place. If he looks at one area near the horizon, he might see a small pond, but if he looks away then back again, the pond might no longer be there. Not as though it suddenly dried up, but as if it were never there to begin with.

It feels like he's inside a very large reality marble.