What should a young man do if a drop of urine comes out of him immediately after urinating, and he believes that most of his prayers over the past eight months were without Wudu?

You must wait until the flow of urine stops after relieving yourself, then perform istinja' (washing the private parts) and wudu' (ablution). You must repeat the prayers that you are certain were invalidated by the emission of urine during the prayer or before it after performing wudu'. As for anything else, the original presumption is that it is valid, and there is no obligation to repeat it.