How is a mature girl who died by burning, and whose body was completely disfigured, to be washed? And is it permissible for men who are not her mahram to wash her, knowing that women washing her might cause distress?

This girl should be washed if possible. If there is fear that her body will disintegrate, she should be given a dry ablution (tayammum) by the person performing it striking their hands on the earth and then wiping her face and palms with them. Then, she should be shrouded and prayed over.

If washing the deceased is not possible due to lack of water or fear of the body disintegrating, then tayammum should be performed.

As for who should wash her: if she does not have a husband, women should wash her. The priority is a female mahram relative, then a non-mahram female relative, then a non-relative woman. If no women are available, the closest male mahram relatives should wash her, in order of proximity. If there is no one available to wash her from among women or male mahrams, the majority of scholars hold that she should be given tayammum and not washed. Some opinions state that she can be washed from over her clothes, with the washer's hand wrapped in a cloth and with averted gaze.