Is the prayer of an unveiled woman accepted, despite her commitment to prayer, fasting, and attending religious seminars, knowing that she only wears the hijab during prayer?

Your prayer is valid if you fulfill its pillars and conditions. However, your not wearing the hijab is a grave sin, based on the Prophet's (peace be upon him) saying: "The worst of your women are the mutabarrijāt (those who display their adornments) and the mutakhayyillāt (those who walk with pride), and they are the hypocrites." And also his saying: "Any woman who takes off her clothes in other than her home has torn the veil between herself and Allah Almighty." Therefore, you must hasten to repent and wear the hijab.