What is the ruling on the cessation of blood after (40) days from delivery, but later continued sporadically during two days of Ramadan?

Once postpartum bleeding (Nifas) ceases, and the woman is certain that it won`t reoccur, then she becomes ritually pure and so she is free to make Ghusl (purificatory bath), pray, and fast. If the bleeding reoccurs before fifteen days from its cessation, and before the end of (60) days after delivery, then the ruling on postpartum bleeding is effective, and her fasting and prayer are null and void, thus she must make up the fasting that she missed and not the prayer during those particular days.

Is a menstruating woman obliged to pray during menses, and should she make up missed prayers?

All perfect praise be to Allah, The Lord of The Worlds                                                                                                                                                                        A menstruating woman is prohibited from prayer during her menses, and she isn`t obliged to make up missed prayers. And Allah Knows Best.

If someone regularly fasts the six days of Shawwal, are they obligated to fast them every year?

A person is not obligated to fast the six days of Shawwal every year, even if they have made it a habit. However, someone who regularly performs a good deed should not abandon it as long as they are able.

Is it permissible for a woman to perform the obligatory prayer immediately after the adhan and before the Iqamah is performed in the mosque?