Is it permissible to consider the discharges from a woman as normal vaginal moisture when in doubt as to whether they are madhiy, and what is the ruling concerning previous prayers if that was incorrect?

Al-madhy is a thin, white liquid that is discharged when aroused. What is discharged without arousal is considered normal vaginal discharge (vaginal wetness). If you are unsure whether what came out is madhy or discharge, the default is that madhy has not been discharged, and your previous prayers are valid. However, purifying yourself from this discharge is good, to avoid the differing opinion of those who consider it impure.