What is the madhhab that should be followed regarding swallowing phlegm while fasting, what is the ruling on adopting the view of the Hanafis on this issue, and is it sufficient to make up for the days on which phlegm was swallowed?

In summary, swallowing phlegm does not invalidate the fast according to the Hanafis and Malikis. However, it does invalidate the fast according to the Shafi'is and Hanbalis if it reaches the apparent part (the mouth for the Hanbalis, and beyond the exit of the letter 'Haa' towards the mouth for the Shafi'is), provided one knows it invalidates the fast and is able to expel it. So, whoever swallows it knowingly and while able to expel it, their fast is invalidated and they must make up for it, according to the Shafi'i and Hanbali schools, and this is more cautious. There is no make-up required for it according to the Hanafis and Malikis, and it is permissible to adopt this view by way of taqleed (following a qualified scholar), while noting the impermissibility of selectively following dispensations from every school.