Is taking money from one's mother considered a forbidden gift if the request is based on need or lack thereof, and is it permissible for a mother to cover the costs of her son's surgery if he is well-off, and how can one differentiate between this and a forbidden gift?

If you have enough [money] or are not in need of money, then asking your mother falls under the dispraised matter, and prophetic hadiths indicate this, such as: "Whoever asks people for their wealth to accumulate it is only asking for live coals, so let him ask for little or much," and "A man keeps asking people until he comes on the Day of Resurrection with no piece of flesh on his face," and "Whoever asks people [for money] when he has what suffices him, his asking will come on the Day of Resurrection as scratches or abrasions or bruises on his face." The mother must be fair among her children in gifts and grants, just like the father, for the Prophet, peace and blessings be upon him, said: "Fear Allah and be just among your children." So, if you have sufficient money for the operation costs, then what you take from your mother is considered a gift that it is not permissible for her to give to you without fairness among your siblings, nor is it permissible for you to ask for it when you have what suffices you.