When Kazuki was sold to make the Thanatos system, the system creators were faced with a dilemma:
how to keep the brain alive.
Their original intent was to
cut off the brain and hook the organ directly to the machinery
But then they would have to deal with a "little" problem:
they would need to supply nutrients, oxygen, antibodies, leukocytes, and all sorts of stuff to the brain.
That would require additional machinery/technology, but then they realized that
a human body already does all that, you just have to shove food and oxygen through the mouth and nose.
So they decided to ditch their original plan and
just hook Kazuki's brain indirectly to the machinery, and keep the body intact in life support fluid (think of Evangelion's LCL).
About Kazuki's body not aging, she was 12/13 years old when the accident happened.
Her body was not frozen. It was kept in a vegetative-comatose-ish state. In the visual novels, she is very debilitated when rescued by JB, and had to be carried out of Ichigaya by the German blonde.
Also a spoiler of future episodes, so don't read below:
the hook in her hand (the one she injuried in the bus crash) is fake. Her arm/hand is fine and she thinks she is making a great pun, but Kazuki is running for worst sense of humor in a VN/anime character ever. Who gave her that grappling hand in the suspended animation chamber, it is stuff for another question.
According to wikipedia, females end puberty earlier than males, and reach an adult body earlier too:
Maximal adult height is achieved at an average age of 15 years for an average girl and 18 years for an average boy.
So, we can assume Kazuki grew around two more year's worth since the accident. Her body frame was always petite and she was precocious in several aspects, why not puberty? She was around the same size as Amane during the accident, so maybe her growth spurt had already happened by then.
And to boot:
She was sexually active since a very tender age. Her favorite food is Yuuji (eden ep.6), nuff said.
Probably that caused her puberty to have an early onset.