Is it permissible to sleep in clothes that have dried madhi on them, then change them without washing the private parts before prayer, and is it obligatory to repeat the prayer?

Madhy (pre-seminal fluid) is impure (najis), and the correct approach is to wash whatever part of the body it has touched before prayer. If someone prayed with it out of ignorance or forgetfulness, their prayer is valid, and they do not need to repeat it. However, if someone prayed with it intentionally, their prayer is invalid and must be repeated.