Is the prayer of one who slightly raises his head and body after the first prostration, then returns for the second prostration without fully sitting upright, valid? And is sitting upright after the first prostration a condition for the validity of prayer?

If a worshiper does not sit with ṭumaʾnīnah (tranquility/stillness) between the two prostrations, their prayer is invalid because ṭumaʾnīnah between the two prostrations is a pillar of the prayer. One who does this must be advised with wisdom and good counsel. If they do not respond after a full explanation, then there is no blame upon the advisor, for they have fulfilled their duty.