What is the ruling of Islamic law on donating bone marrow to cancer patients using the two aforementioned methods, and which of them is better, and is the donor rewarded even if the patient is not a Muslim?

It is permissible for a Muslim to donate stem cells to a non-Muslim who is not a belligerent, and the Muslim will be rewarded for this donation if they intend to do good, based on the Almighty's saying: (Allah does not forbid you from those who do not fight you because of religion and do not expel you from your homes - from being righteous toward them and acting justly toward them. Indeed, Allah loves those who act justly). Furthermore, there is no harm in either method of extracting and separating marrow; the easier and less risky option for the donor should be chosen.