Is it obligatory to repeat the prayer if the worshipper becomes certain that madhiy (prostatic fluid) exited after the prayer, without having anticipated it beforehand? And is the prayer considered valid if the worshipper becomes certain that madhiy exited after the prayer, after having doubted it before the prayer and prayed in that state?

It is advisable to avoid stimulants of desire, strengthen one's connection with God, lower one's gaze, and fast. If you suspect pre-ejaculate (madhy) has exited, the default assumption is that it has not, so you may continue with your prayer unless you are certain that your ritual purity has been invalidated. You are not required to investigate; rather, you should act upon the certainty of your purity. However, if you become certain of its exit after the prayer, it is attributed to the latest time it could have possibly exited. If its exit could have occurred after the prayer, then your prayer is valid. But if it could only have occurred before or during the prayer and you did not perform ablution (wudu'), then your prayer is invalid and must be repeated after performing ablution. If you performed ablution and prayed, then found its traces before the prayer, your prayer is valid.