Is prayer obligatory while menstrual bleeding continues for a month and two weeks, knowing that it is menstrual blood with the description mentioned?

The maximum duration of menstruation according to the majority of scholars is fifteen days, and anything exceeding that is considered istihadah (definition) (non-menstrual bleeding). A woman experiencing istihadah has three situations: 1. If she has a previous habit (regular cycle): She refers to it, and anything beyond it is istihadah. With istihadah, she performs ablution (wudu') for each prayer after its time has begun and takes precautions (e.g., uses a sanitary pad). 2. If she does not have a habit but can distinguish (between menstrual and non-menstrual blood): She acts according to the distinction. She refrains from prayer and fasting for the duration she distinguishes as menstruation, and anything else is istihadah. 3. If she is neither accustomed nor able to distinguish: She observes the common habit of women (six or seven days), then performs a ritual bath (ghusl (definition)) and acts as a woman in istihadah.

Therefore, if you are experiencing istihadah: If you have a previous habit: You observe the duration of your habit, then perform ghusl, perform wudu' for each prayer, and take precautions. If you are neither accustomed nor able to distinguish: You observe the common habit of women (six or seven days), then perform ghusl and do what is required of a woman in istihadah. And the prayers you missed during that period must be made up (Qada') according to the majority of scholars.