In the answer to question no. 108125 we discussed bone marrow and quoted the statement of the Islamic Fiqh Council that it is permissible to take it from adults if that will not cause them any harm.
The Muslim will be rewarded for donating it if his intention is sincerely for the sake of Allah and he intends to do good to the person to whom it is donated, whether he is Muslim or non-Muslim, on condition that he is not a harbi (a non-Muslim in a state of war against Islam), because there is nothing wrong with showing kindness to a kaafir who is at peace with the Muslims. Allah says (interpretation of the meaning):
“Allaah does not forbid you to deal justly and kindly with those who fought not against you on account of religion nor drove you out of your homes. Verily, Allaah loves those who deal with equity”
The scholars of the Standing Committee for Issuing Fatwas were asked:
Is it permissible to transfer blood from one person to another even if they are of different religions?
They replied: If a person is sick or is very weak and there is no way to treat him or help him except by transferring blood to him from someone else, and that is a way to save him, and the experts think it most likely that it will benefit him, there is nothing wrong with treating him by transferring blood from someone else to him, even if they are of different religions. So blood may be transferred from a kaafir, even if he is a harbi, to a Muslim and from a Muslim to a kaafir who is not a harbi. But in the case of a harbi, he is not under the protection of sharee‘ah and it is not permissible to help him. End quote.
Fataawa al-Lajnah al-Daa’imah, 25/66
See also the answer to question no. 12729.
With regard to your questions about the two methods you described of extracting marrow and separating it, it seems that there is nothing wrong with either of them. Determining which of them is better should be left to specialist doctors and the method which is easiest and least risky for the donor should be chosen.
And Allah knows best.