Is a specific order required when washing the penis and testicles [for a male] or the vulva [for a female], and does a state of ritual impurity necessitate re-washing the penis and testicles or the vulva before ablution, and is continuity (al-muwalat) obligatory between them?

Washing the penis and testicles during Istinja' (cleaning after defecation/urination) is not obligatory according to the more preponderant opinion. Rather, what is obligatory is only washing the soiled area. The Hanbalis, however, are of the opinion that washing the penis and testicles is obligatory, and there is no specific order for washing them. As for one afflicted with persistent seminal discharge (madhy سلس المذي), he should perform ablution (wudu') for each prayer after its time has begun. This ablution is valid for both obligatory (fard) and supererogatory (nafl) prayers. His purity is not invalidated except by the expiry of the prayer's time or by another impurity (hadath) other than the persistent discharge. He should also take precautions by tying a cloth or similar item.