Is it obligatory to repeat the prayer every time one discovers the discharge of prostatic fluid (madhy) after praying, as a result of an erection during istinja' (washing after urinating or defecating) without lustful thoughts, and does looking at the private parts after ablution (wudu') and before prayer to confirm invalidate the ablution?

You may be afflicted with waswasah (whispers/obsessive thoughts). If you are certain that madhy (definition) (pre-seminal fluid) exited before or during the prayer, and you prayed in that state, then your prayer is invalid and you must repeat it. However, if it is merely a doubt, do not pay attention to it. You are not required to inspect to ascertain if anything has exited, and the default is that nothing has exited. If you touch your private part without a barrier, your wudu' (ablution) is invalidated, according to the more preponderant opinion. If it is with a barrier, it is not invalidated. If the emission of madhy occurs frequently such that you cannot find time to pray with proper purity, then your ruling is that of one afflicted with incontinence (sals). In this case, you perform wudu' after the time for prayer begins and then pray. However, if the emission of madhy stops for a period sufficient for purification and prayer, then you must pray during that time.