Was my mother accountable for not praying the 'Isha prayer due to severe pain before her death, and how can atonement be made for this sin on her behalf? What is the meaning of my mother falling to the ground and vomiting coffee-colored material after her death? And is she considered to have died from an internal illness (mabṭūnah) given her suffering from severe stomach pain before death?

There is no sin upon one who delays the prayer past its initial time if they intended to perform it and died before doing so. If the mother died due to stomach pain, it is hoped that she is among the martyrs, due to the Prophet's (peace be upon him) saying: "The martyrs are five: the one who dies of plague, the one who dies of a stomach disease, the drowned, the one who dies under a collapsing building, and the martyr in the cause of Allah." There is no legal (Shar'i) indication for vomiting a coffee-colored substance without hearing the sound of its expulsion.