Y

She was technically the first friend K ever had and has been and always will be in love with him.

Personality
Y is for Yandere.

Authority
Her ability is "save state" and is a Rule type authority. She needs to make certain agreements with people and the instant they die a violent death, they get returned to a certain state in time. There are obvious costs (it can only be used several times per day), and she can't use it on herself.

Clearly, it is not super practical in battle, and is mainly a plot-driven ability to make K a bit more invincible.

Weapon
She uses a scarf and is very much similar Agent 10 from Black Cat. There are many ways to use a scarf to kill someone: cutting them and choking them are the basic two. Her scarf is made of several inter-weaving fibers that can resist bullets.

In fact her scarf is actually part of a bit of clothing that K once gave to her for her birthday (he's long since forgotten about this). Thus, that scarf holds such a strong meaning to her that she can use her "save state" ability to return it to normal.