What is the ruling on the prayer of a woman who suffers from continuous vaginal discharge that is white and yellowish and stringy, and finds it difficult to perform prayer and ablution outside the home, and is the pulsing sensation she feels in her lower abdomen upon seeing fighting/beating considered masturbation?

White vaginal discharge is pure and does not necessitate istinja' (washing private parts after urination/defecation), but it does nullify wudu' (ablution). As for yellow discharge, it is impure and considered menses if it occurs during the usual period or is connected to blood. If it is not menses, it still nullifies wudu' and requires cleansing whatever it touches. If the discharge is continuous, the woman is in the ruling of one with sals (incontinence), so she performs wudu' for each prayer after its time has begun and prays the obligatory and supererogatory prayers until the time for that prayer expires. The feeling you described when seeing a young man is not masturbation, but it is necessary to avoid whatever arouses desire and to lower the gaze from non-mahram men for fear of fitna (temptation/tribulation).