Is a girl who has reached the age of fifteen and has not shown any signs of puberty, and neither desires men nor is desired by them, obliged to observe hijab in front of non-mahram men and refrain from shaking their hands?

If a girl reaches the age of 15, she is treated as an adult, even if other signs of puberty have not appeared, because what matters is the puberty that has occurred. She is then required to observe what is obligatory for adult women, such as wearing the hijab and not shaking hands with or being in seclusion with non-mahram men.