How are the Fajr prayers, which were prayed at the first call to prayer without knowing the (correct) number (of rak'ahs), to be made up? And are the current prayers accepted before making them up?

Prayer performed before its prescribed time is not valid. The time for Fajr prayer begins with the appearance of the true dawn (al-fajr al-sadiq) and extends until sunrise. The false dawn (al-fajr al-kadhib) precedes the true dawn by about twenty minutes and appears as a vertical light. The true dawn, however, is a horizontal whiteness spreading across the horizon.

If the questioner's prayer was performed before the true dawn, it is invalid. They are obliged to make up these prayers immediately, estimating their number based on their best judgment and arranging them by intention. The invalidity of the Fajr prayer does not affect the validity of the other prayers. However, in this specific case, if there was ignorance regarding the time and no negligence, then no make-up prayer is required.