What can I say to people who ask about a girl who is not my daughter so that they understand, and does the meaning of the Hadith: «No man who knowingly claims to be the son of other than his father but has disbelieved» refer to minor disbelief, and what should I do about the fatwa that I have not yet received?

There is no harm in answering about the child with the phrase "orphan" or similar, as long as you do not intend to report something contrary to reality. What is forbidden is spreading the lineage of a girl to other than her parents. As for the hadith, "He has disbelieved who claims descent from other than his father," what is meant by it is disbelief in blessings or minor disbelief, unless one deems it permissible.