1. Apparently, Sakuya Izayoi is not her real name, according to Perfect Memento in Strict Sense.

2. She bears a strong resemblence to Yumeko, since both are blade-throwing maids who serve demon-like masters.

3. Sakuya can also use her powers to accelerate time, such as making bamboo flowers bloom instantly, even though this would normally take 60 years to grow.

4. HER EYES CHANGE FROM RED TO BLUE WHAT IS HAPPENING

5. A popular theory of the maid's origins is that Sakuya was a vampire hunter. One day, she came upon the Scarlet Devil mansion, obviously trying to hunt Remilla, probably. Of course, Sakuya failed, but Remilla spared her life, probably due to wanting to have Sakuya's powers for herself.

6. In Imperishable Night, it is indicated that Sakuya went mad in Good Ending #3 after Kaguya shines the light of the true full moon. Remilla is worried for her, but the maid does not seem affected by it. Shortly after, ZUN drew a picture of Sakuya with red eyes, further implying that the unfortunate maid did indeed go mad in that particular ending.
Sakuya's red eyes (artist: ZUN):

(Sorry if the picture doesn't show up!)

7. This isn't official or anything, but at the end of stage two this event happens, which can be interpreted as quite disturbing (well, I found it disturbing on my first play through as them anyways...):
Sakuya: ...speaking of which, why are we headed in this direction?
Remilla: Hm? Refueling.
Sakuya: ......
I interpreted this as Remilla was going to refuel by sucking Sakuya's blood, which I found quite...unsettling.

8. It is heavily implied that Sakuya cooks humans for Flandre and Remilla. Ech, very unsettling indeed.

9. Sakuya, although probably a human herself, is very set apart from them due to her time manipulation powers.

10. Sakuya is one of the few people to know who Kaguya and Eirin were. Eirin states that she was surprised to see Sakuya. Connection???

(A/N: Feel free to request a specific character/topic! Also, Some of these facts can be found on Wikipedia, others I already know about. Good day my friends)