Is it permissible to marry a girl who has run away from her family, without the permission of her family and mine, knowing that the girl has gone through difficult circumstances and wishes to escape her reality?

If the girl's family mistreats her, and her maternal uncle committed fornication with her, then they are in error and should be advised. They do not have the right to force her to marry someone she does not desire. She should try to convince them or take the matter to a Sharia judge. As for you, you erred by inciting her to run away, and it is not permissible for you to marry her without her guardian's permission. If marriage to her is not possible, then cut off your relationship with her, as a relationship between a Muslim man and a non-mahram woman is not permissible.