Is my betrothal to an adopted girl via Skype, with the approval of her adoptive guardian, considered a legitimate betrothal? Is it permissible to conceal her adoption from my family and from the judge when the marriage contract is concluded? Is it permissible for her dowry to be a Sura from the Holy Qur'an?

First: Adopting children and attributing them to other than their real fathers is forbidden. The lineage of this girl must be corrected to her true father. If he is unknown, then to a fictitious name that suggests devotion to Allah Almighty. This must be amended in official documents as much as possible. Relatives should be informed of her true lineage if official amendment is impossible.

Second: Since you have proposed to this girl, it is forbidden for anyone else to propose to her as long as the engagement is ongoing. A mature woman may propose for herself.

Third: It is permissible to conceal the fact of her adoption from the family if the benefit necessitates it.

Fourth: If her father or guardian is known, he is the one who officiates the marriage contract if possible. Otherwise, it is the Sharia (definition) judge. If that is impossible, then the adoptive father or any other Muslim can undertake her marriage.

Fifth: What you mentioned about buying furniture and a gold gift can serve as a dowry for her, and an agreement can be reached on that, as there is no limit to the dowry.

Sixth: The girl's request for her dowry to be the memorization of a surah (definition) from the Quran is not valid as a dowry. Rather, the gold gift is the dowry. She can stipulate that you memorize the surah as a condition in the marriage contract.