Is it obligatory to repeat the prayers that were performed over 13 years while unaware of the necessity of ritual bathing (ghusl) and the removal of impurities that invalidate ablution (wudu')? And is it necessary for a person to have the intention (niyyah) to make them up, or for someone else to make them up on their behalf in the event of death before they are repeated?

If the discharge is vaginal wetness, then it nullifies ablution (wudu') but is pure (tahir) and does not require washing. Your prayers are valid if you perform ablution for it. However, if you did not perform ablution for it out of ignorance, scholars have differed regarding the necessity of repeating the prayer. You may choose the precautionary approach, which is to make up (qada') the prayers.

If the discharge is impure (najis), such as madhy (pre-seminal fluid), and you neglected to remove it or perform ablution for it out of ignorance, the majority of scholars believe that repeating the prayer is necessary, while some scholars do not. If you choose to make up the prayers as a precaution, do what you can without hardship. If death overtakes you while you are in this state, then you are upon goodness, and no one is obligated to make up prayers on your behalf.