What is the difference between menstrual blood, postpartum blood, and irregular vaginal bleeding (dam al-fasad)? And is it obligatory to perform ghusl, pray, and perform wudu for every prayer in the case of irregular vaginal bleeding, knowing that the bleeding continues for a long time after a two-day cessation from the menstrual period, followed by a D&C procedure?

The first blood is menstrual blood. The blood that returned two days after purification and continued for 23 days is corrupt blood (istihada) and cannot be appended to the first blood, because the total exceeds 15 days. Nor is it considered new menses due to the absence of the minimum period of purity (15 days) between it and the first blood, unless you distinguish menstrual blood during the returning period. Menstrual blood prohibits prayer, fasting, circumambulation (Tawaf), touching and reciting the Qur'an, staying in the mosque, and sexual intercourse. As for istihada blood, it does not prohibit any of that. Rather, the woman must perform ghusl after menstruation, purify herself, and perform ablution for every prayer.