Chances are, who ever designed it just hodge-podged it based on real world buildings. Those triangle-peaked windows in the roof probably have technical names, along with the style of roof itself which looks familiar. Closest I can find is that it appears similar to a "mansard roof", akin to some found on old fast food restaurant franchises. Any architects on the board?
I rather wondered that, but Aerith does seem to be a general benefactor in the neighbourhood. I guess I also quite like the fact that after Cloud's initial "Nice place", everybody completely ignores the improbability and incongruity of the Gainsborough house.
Hi there - I asked what kind of house it was to someone in the fandom who knows architecture. She said it's an "Octagon House" https://en.wikipedia.org/wiki/Octagon_house
However, while you can find octagonal houses with mansard roofs all over the world, and certainly in Europe, the "Octagon House" was a turn of the 19th/20th century North American phenomenon. We don't know whether the person who designed the Gainsborough was directly inspired by American Octagon Houses, or by something else.
It's gonna become A Thing, I'm sure. Looking forward to it.
As to why her place is so nice vs the slums, we don't actually see (in the remake, that is) other residences apart from the orphanage in Sector 5. For all we know, where the other people live could also be nice (sans flowers anyway, since thats particular to Aerith). Whether that also means the same land area for everyone, I'm assuming not, but I also assume Aerith gives a good bit of her money away (she works "for fun" a lot of the time after all) so people are less likely to be mad.
It's a bit of a walk to their house, and the plants slowly get more plentiful as you get towards it.
Her house is the far left of this map: (the cluster of icons in the right-middle is the main part of town from the OG)
So it eases into it a bit, but it is still pretty striking