Is all the reward for Hajj recorded solely for the father of a friend, with nothing for the one who performed Hajj? And is it permissible to perform Umrah for one's parents during Hajj on behalf of another?

The illness of a pilgrim does not affect the validity of their Hajj, as long as they do not omit any of its pillars. It is permissible to perform Hajj on behalf of a deceased person or someone incapacitated by a chronic illness or old age. It is also permissible to perform Umrah on behalf of parents from Mecca, with two points to note: First, it is not permissible to enter into the state of ihram for Umrah while performing Hajj, including during the days of Tashreeq. Second, one must enter into ihram on behalf of another from the miqat of the person for whom the Umrah is being performed.