Is the questioner sinful and is expiation obligatory for her for uncovering her face before the doctor and nurses due to the necessity of treatment, and is she obligated to make up the days she did not pray due to the surgery and then menstruation, considering her delay in performing ghusl after menstruation?

If the face is uncovered out of necessity, there is no sin. Otherwise, one must seek forgiveness and repent. As for abandoning prayer, it is a grave sin, and missed prayers must be made up with repentance and seeking forgiveness, while taking advantage of dispensations when unable to fulfill some conditions, pillars, or duties of prayer.