What is the ruling on one who vows not to sleep before the Asr prayer so as not to miss congregational prayer, then sleeps, and is he required to fulfill this vow, and what is the ruling on the days he missed congregational prayer?

If you miss congregational prayer or the prayer time due to sleep, there is no blame or sin upon you if you took measures to wake up and tried hard to do so, because Islamic law excuses the sleeper. Evidence for this is the hadith narrated by Al-Bukhari and Muslim from Abu Qatadah, that the Prophet (peace be upon him) and his companions missed the time for Fajr prayer during a journey. The Prophet (peace be upon him) then said: "Verily, there is no negligence in sleep. Negligence is only on him who does not pray the prayer until the time for the next prayer comes."

As for the vow you made but did not fulfill, you must offer an expiation for breaking an oath, which is: feeding ten poor persons, or clothing them, or emancipating a slave. If you are unable to do any of these, then you must fast for three days.