We have no sister, so my mother and father agreed to adopt a girl child and they adopt a girl baby from my uncle (my mother's brother), now she came to the age of marriage, can our family including myself have the right to decide whom to she will marry or we have to ask from my uncle?, secondly we are responsible of her marriage ( giving dawry to her) or not?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.

If you mean by adoption attributing this girl to your father, this adoption is prohibited as previously clarified in Fatwa 82371. Adoption does not change the reality at all, so parentage of this girl remains for her true father who is her matrimonial guardian and responsible for her marriage. Therefore, it is not permissible for your father to choose a husband for her or give her in marriage without permission of her matrimonial guardian.

On the other hand, the dowry is the woman's right over her husband, not the opposite. If it is your custom that the woman's family pays a dowry to the husband, this custom is against the Islamic Sharee‘ah and it is not permissible to continue practicing it. There is no harm that your father gives her a gift out of benevolence or gives it to her husband if she gets married.

Moreover, if you mean by adoption taking care of and being kind to the girl, this is a good act the doer of which will be rewarded. Allaah The Almighty Says (what means): {And do good; indeed, Allaah Loves the doers of good.} [Quran 2:195]

It should be noted that the girl remains a non-Mahram to you, your father, and your brothers, so you are not allowed to shake hands with her or be in seclusion with her or the like, unless there is a reason that makes her a Mahram to you such as suckling.

Allaah Knows best.