The Ruling on Intention in Voluntary Fasting and Hajj

I have learned that if a Muslim fasts a voluntary day with more than one intention, the reward is according to the intention, based on the hadith: And Allah knows best. My question is: Is it permissible for a Muslim to perform the obligatory Hajj with two intentions, such as performing Hajj with the intention that it is for himself and for one of his parents? May Allah reward you.
Answer: This differs. Hajj is not performed for more than one person. If he intends it for himself, it is for himself. If he intends it for his father, it is for his father, and he is rewarded for his dutifulness to his father. The same applies to 'Umrah. If he performs 'Umrah for his deceased father, or for his deceased mother, or for those who are unable due to old age, he has a reward for that, because he has been dutiful to them through this act, and he is rewarded for this. However, Hajj is not performed for two people; Hajj is for one person, and 'Umrah is for one person. If he intended it for himself, it is for him. If he intended it for his father, it is for his father. If he intended it for his mother, it is for his mother. If he intended it for both of them, for himself and his father, it becomes for himself only; it does not count for two people.
Therefore, it is recommended that whoever wants to be dutiful to his father should make the Hajj for him alone. Likewise, for his mother, he should intend it for her alone, and he is rewarded for his dutifulness to them and his kindness to them.
As for some acts, the intention can vary in them. For example, if he fasts on Thursday for the virtue of Thursday, and because he sees in it energy for some of his works and strength for some of his works, and for other reasons, there is no harm. If he fasts on Thursday for its virtue, and because he strengthens himself with it for a work, or because he feels comfortable in it and sees energy or another benefit in it, then he did it for this and that, and there is no harm.
Likewise, if he prays Tahajjud at night because he loves to worship at night, and because he sees in it health for his body and digestion of his food, and the like of that, may Allah gather good for him. But it is not like the one who prays for Allah with the sole intention; that one is more complete. Yes.
The presenter: And what about one who chooses the white days, for example, to make them a place for making up what he missed from Ramadan due to illness, travel, or a natural excuse?
The Shaykh: It does not appear to me in this case that he has anything other than making up the fasts. He has only the making up of the fasts. We hope for him good if he intends by this that he fasts this, perhaps... We hope that good will be attained for him, if Allah wills. We hope. Like the one who makes his make-up fasts on Thursday and Monday for the sake of the virtue of Monday and Thursday, it is hoped that he will be given a reward in this. It is hoped for him, but it does not harm him. Yes.
The presenter: May Allah reward you.