Is it obligatory to repeat prayers that were missed due to neglecting one or more obligatory prayers, or those that were performed with clothes in which impurity was mixed with purity, or those that were performed with vaginal discharge based on a mistaken understanding?

Prayer does not become obligatory at the age of ten, but rather upon reaching legal puberty (menstruation, ejaculation, growth of coarse hair, or reaching the age of fifteen). If you are unsure whether you neglected an act of worship before or after it became obligatory, the default is that you are free from liability. Washing pure clothes with impure ones in a small amount of water is permissible as long as the water does not become impure. Doubt about discharges should be treated as you wish. Not performing ablution after discharges due to ignorance does not necessitate repeating the prayer, to avoid hardship.