"Ruined Western Mansion" is not the official name, but a generic term, and how one would most likely call it in Japanese. The Prismrivers' profile called it "poltergeist residency" 騒霊屋敷. For this chart, "Ruined Western Mansion" should be sufficient.
You have made good progress on the chart. It's my time to chime in. I'll focus on the relationships now, and examine descriptions later.
Locations:
Renko and Merry lives not only outside of Gensokyo, but also in near future. It's better to put a stronger emphasis on how they are from an entirely different world.
Iku's profile says she lives "inside the clouds", while the name of her stage is 玄雲海, which seems to have been translated as "Mystic Clouds" in the English patch? I think you should just use "Inside the Clouds".
Kasen doesn't live in a pocket dimension. Her house is located on the Youkai Mountain.
I think Rumia can be placed in the Forest of Magic, but that's not very important.
Characters:
Further remove the fanon parts: no need for Lily Black, as it's just Lily White in different clothing; the description for the dolls shouldn't mention Shanghai and Hourai, perhaps something like "still not sentient" would be better.
Remember to add Namazu's in-game sprite, and change its background to "fauna". (Given its insignificance, I'd actually put in major characters like Tsukuyomi before Namazu.)
It's inappropriate to mark Utsuho as half-divine. According to Kanako in SoPM, she's more comparable to a "mobile shrine". In a way, Shou is much closer to divine than Utsuho (I still don't think Shou should be marked "Divine").
There's no reason Futo is not categorized a hermit. Shikasen is definitely a type of hermit.
The generic "kappa" character feels clunky, but I can't think of a better way to represent it without making large changes, either.
Relationship:
IIRC, there's nothing in canon that says Yukari treats Chen as a pet.
Remember to change Miko's relationship to Seiga to "Former Teacher" for consistency, and other consistency checks such as "Friends".
The "Hostile" relationship between Sakuya and Alice is unnecessary. They both attend Hakurei Shrine parties, after all, and since Alice prefers talking to humans, she must have talked to Sakuya a lot.
I'm also ambivalent about the "Dislike" line between Sunny and Lily. Sunny feels a bit bad about being defeated by Lily once, nothing more than that, which is quite unlike the relationship between Momiji and Aya.