Does "The Garden of Sinners" share the same world with "Fate" series? Looking back at both The Garden of Sinners and Fate series, I noticed that there are mystic eyes in both series. For example, Rider's Mystic Eyes of petrification revealed Fate/stay night: Heaven's Feel and Shiki Ryougi's Mystic Eyes of death perception from The Garden of Sinners series).
Do they both share the same world?
Yes, Kara no Kyoukai, Tsukihime and Fate all take place in the same universe.
Aozaki Touko from Kara no Kyoukai is the sister of Aozaki Aoko from Tsukihime. Ciel from Tsukihime and Kotomine Kirei from Fate are part of the same organization. In Fate/Zero there's a part about Kiritsugus past relating to Dead Apostles (Vampires), that are the same as the ones from Tsukihime.
Ryougi Shiki from Kara no Kyoukai and Tohno Shiki from Tsukihime have the same type of mystic eyes.
In Kara no Kyoukai there's a magus trying to reach the origin/root by using a spiral of sorts. It's described as the main pursuit of all magi. In Fate, the Holy Grail War was designed to reach exactly this origin/root, too.
Here's an even more comprehensive relations chart: