Is it permissible for a girl to commit suicide before being subjected to rape, and would she be considered a disbeliever in this case, knowing that those who commit suicide may not be in their full senses?

Suicide is a grave major sin, and it is impermissible to commit it, even if the motive is to escape coercion into adultery. Whoever commits this act is not an disbeliever, but rather a disobedient Muslim who has committed a major sin. His matter is subject to the will of Allah Almighty.