What is the ruling regarding the prayer of young girls who have not yet reached puberty, if they pray without a complete hijab (with some of their hair showing), or if they pray while sitting? And is it obligatory for them to cover their hair during prayer?

As long as the girls have not reached puberty, their prayers without a head covering are valid, based on the Prophet's (peace be upon him) saying: "Allah does not accept the prayer of a menstruating woman unless she is wearing a head covering (khimar)." This indicates the validity of the prayer of one who has not menstruated, with her head uncovered. However, their praying while sitting is not valid if they are able to stand; standing is obligatory, based on the Prophet's (peace be upon him) saying: "Pray standing; if you are unable, then sitting; and if you are unable, then on your side."