Is it necessary to wait until the discharges cease to perform Fajr prayer after sunrise, or should it be performed while the discharges are still present?

You are subject to the ruling concerning one afflicted with constant discharge, as long as the discharge persists. Therefore, you should perform ablution after the entry of the prayer time and pray as many obligatory and supererogatory prayers as you wish until the departure of the current prayer time. If you perform ablution for the missed prayer after sunrise, your prayer is valid, and you are not required to wait for the entry of the Dhuhr time or for the discharge to lessen, as making up a prayer is an immediate obligation.