Is prayer obligatory for a woman who had a miscarriage in the third month and underwent a D&C procedure, and did not pray for a week due to pain, or is she required to make up the missed prayers?

Prayer does not fall away from a Muslim as long as their mind is sound. If you stopped praying after the bleeding ceased, you have erred and must make up the prayers immediately. If you stopped praying while bleeding, then if the miscarriage showed signs of human creation, the blood is considered nifas (postnatal bleeding), and you are not required to make up the prayers. However, if it did not show signs of human creation, then the blood is istihadha (irregular non-menstrual bleeding), and prayer is obligatory, and you must make up the prayers.