Is it valid to fast on Mondays and Thursdays with the intention of fasting at the time of suhoor before midnight, and then to sleep through the adhan of Fajr, due to a student's limited time?

The suhoor (definition) is a Sunnah (definition) for whoever intends to fast. Its time begins at midnight and ends at the appearance of true dawn. So, if the meal is after midnight, it is considered suhoor; otherwise, it is not legally considered suhoor. The fast is valid even if suhoor is omitted, though it is preferable to be diligent about it. The intention for fasting made at any part of the night is sufficient. If the fast is a supererogatory one, the intention made during the day is sufficient, and some scholars stipulate that it must occur before zawal (midday).