Is it unlawful for the questioner, an orphan who has only a small pension that barely covers food, to take out a loan from a personal finance organization for the purpose of studying?

If the association pays the student's tuition fees and then collects them back from her in installments without any increase or late penalty, this is permissible. However, if it collects these expenses with an increase, this is usury (riba), which is forbidden. The Messenger of Allah, peace and blessings be upon him, cursed the one who consumes usury, the one who feeds it, its scribe, and its two witnesses. A Muslim should fear Allah and rely on Him to provide him with lawful sustenance.