Does the discharge of fluid upon merely thinking about a man's penis during prayer, without feeling sexual desire, count as madhy (pre-seminal fluid), or as water from istinja (cleaning oneself after urinating/defecating), or as vaginal moisture that does not nullify wudu?

The madhiy (pre-seminal fluid) is discharged upon feeling or thinking about pleasure. However, you should not pay attention to what you feel coming out during prayer, as it is doubtful, and therefore your prayer is valid and you do not need to repeat it. Ibn Baz says: "As long as you have even a slight doubt, do not pay attention to this matter; consider it an illusion."