The island various forms of edification are internally made out of crystal, the structure is shaped both in the macro and microscopic level to be both lightweight and capable of holding up a lot of mass. Most buildings are two store tall, but they could be easily twenty times taller than that before they would need be careful about making the structure keep standing.
However, the "skin" is made of whichever materials they want, there is a preference for stone, but there is variety. Some buildings appear to be made out of living plants, or plants that have been once alive, either case they are unnaturally shaped to fit whatever was the desired aesthetic. There are a lot of statues, and those are made of literally anything, one looks made out of some kind of constantly dripping ice (it doubles as a fountain). Some buildings clash, but the overall style is pleasant. You get the sense that they could have gone for more opulent with gold and jewels, but figure out something that wasn't so garish.
They have spare rooms and buildings, currently being used for storage or other activities. But for the immediate future they are going to the guest wing of the (rather larger) house where Henries and Gabes reside. It's the one with a large statue of Henry and Gabe in an embrace. It appears to be mid-renovation with two Gabes working to change the style to something red-gray with square patterns to something pearly-white with more vertical lines and curved details.