What is the ruling on one who swallowed semen due to obsessive whisperings, then Satan whispered to him that his spit is impure, and that he should wipe his limbs of ablution with soap after finishing it; and is it obligatory for him to perform istinja' (ablution for private parts) upon feeling the discharge of madhy (pre-seminal fluid) merely due to obsessive whisperings?

The cure for intrusive thoughts (waswas) is to ignore them and pay them no mind. Semen is pure according to the majority of scholars, so there is no need to have intrusive thoughts about limbs becoming impure because of it. Whenever Satan invites you to wash what is not prescribed to be washed, such as washing the ablution limbs more than three times, or washing limbs merely due to doubt about their impurity, then turn away from his intrusive suggestions. As for pre-seminal fluid (madhy), the default is that it has not exited, so do not inspect or look at your clothes, and do not rule that your purity has been invalidated unless you have absolute certainty of its exit.