Is the husband's saying: "By Allah, you will not return to study at that university" considered an oath, and what is the ruling if the wife responds: "By Allah, I will return," along with his statement: "Not under my supervision," and his later acceptance of her going? And is the wife considered sinful if she returns to study?

Divorce does not occur by your return to university as long as your husband has not uttered an explicit divorce, nor an implicit one with the intention of divorce. There is no sin upon you as long as your husband is pleased. However, your husband must pay an expiation for breaking an oath, which is: feeding ten poor persons or clothing them. If he cannot find them, then fasting for three days.