If/theories

Shimitsuki's Name
In ED2 and ED3, we know that her real name is Izumi, Shimitsuki would probably mean death (死, Shi) and body (身, Mi) which speculated she had died in a train accident, and also mean to be 4 (四, Shi) and 3 (三, Mi) because 16:03 (4:03 pm) was the time she died.

Shimitsuki's Effects
Shimitsuki's effects description will change into a word of Kanji in other meanings when she is in her room.

Shimitsuki is Virtual Human Being
Shimitsuki in fact is not real, she been made by girl with pigtails, let's call her Viola, so judging by End 3 Viola made Shimitsuki like Artificial Intelligence, but something goes wrong with her and Viola decides delete her creation.