Is it permissible for a wife to pray, fast, and for her husband to have intercourse with her after a miscarriage and the discharge of blood for more than 20 days, knowing that the color of the blood has changed?

If the fetus aborted by your wife showed signs of human creation, then the blood she sees is nifas (postnatal bleeding), and she must refrain from fasting, prayer, and intercourse until the nifas ends, which is a maximum of forty days. However, if it did not show signs of human creation, then the blood is fasad (irregular bleeding/istihada), and she must pray and fast, performing ablution for each prayer after its time has begun. She must also make up the prayers she missed during this period. The minimum period for human creation to become apparent is eighty days from the beginning of pregnancy.