What is the ruling on a girl's excessive discharges and their effect on ablution, the validity of prayer, and the purity of clothes?

White or clear vaginal discharge (vaginal moisture) is pure but nullifies ablution. Ablution is required for prayer when it exits, but nothing is required if there is doubt about its exit.

If its exit is continuous without interruption, then your ruling is the ruling of one afflicted with incontinence; perform ablution for prayer after its time has begun and pray with this ablution both the obligatory and supererogatory prayers.

As for yellowish or brownish discharge, it has a different ruling.

It is not permissible to delay prayer beyond its prescribed time.