Is my action correct in deeming the first period as menstruation and the second as irregular bleeding—despite the difference in the duration of each—due to continuous bleeding after childbirth and breastfeeding, and is it permissible for me to fast and have intercourse during the period of irregular bleeding?

If menstrual bleeding continues for seven days, then stops for seven days, then returns for five days, the total duration exceeds 15 days, which makes the questioner a woman with istihadha (non-menstrual vaginal bleeding). She must refer to her previous habit (of menstruation). If she does not have a habit, she should act based on discernment (tamyiz). If she cannot discern, she should consider six or seven days as menstruation based on investigation (taharri). She should perform ghusl (ritual bath) after the completion of the menstrual period, and pray and fast during the period of istihadha, performing wudu (ablution) for each prayer after its time has entered, and taking precautions. It is permissible for her husband to have intercourse with her during the period of istihadha.