What is my duty towards my sister, who I don't know if she has reached puberty or not, and who goes out immodestly dressed, and who asked for my help in styling her hair before she went out?

The brother must protect his sister from temptations and teach her the rulings of Sharia, for Allah Almighty says: {Protect yourselves and your families from a Fire}. If the girl reaches the age of ten, her 'awrah ( منطقة في الجسم يجب أن تُستر ) in front of non-mahram men is like that of an adult woman. The brother must prevent his sister from going out unveiled and beautified if she reaches ten or if he fears temptation for her. If he is unable to prevent her, he must denounce her action and not assist her in the wrongdoing. However, if she is under ten and there is no fear of temptation for her, there is no harm in styling her hair.