[The oxygen seems to help, and Conan relaxes, just a little bit. Kaito needs sugar, vitamins, and fluids, but he isn't willing to leave the older boy alone to go get food until he's sure that Kaito won't pass out. There isn't much more he can do about the wounds (they've stopped bleeding now, at the very least), so that leaves explanations for the time being.

Hopefully Kaito's coherent enough to listen to them this time.]

This place is called the Mansion. We don't know who brought us here or who made it, but time doesn't seem to pass at home while we're here; we think it's another world or a separate dimension. While we're here it gives us food and a place to sleep and anything else we need, like the bandages I got you. And when it sends us back home, we go back to the exact time and place that it brought us from.