Is it permissible for a widow to receive a monthly income from a charitable organization to complete her studies, given that she is not in financial need and lives in her father's house, but she prefers not to ask him for money out of consideration for his circumstances?

If the money is from zakat (definition), then for it to be permissible to take it, the knowledge you are acquiring must be Islamic (shar'i) or from the fard kifayat (communal obligations), and you must be poor and in need, and earning a living must prevent you from seeking knowledge. However, if the money is from charity (sadaqah (definition)), then its scope is wide. You must inform the association about your situation and the type of knowledge you are studying. It is preferable to combine seeking knowledge with a suitable job to maintain self-sufficiency.