Through. Damage to the fourth cranial nerve. When this nerve is damaged, the eye on the same side will point higher than the other eye.
Brainstem. Brain centers that control alignment of the eyes are located in the brainstem (lower part of the brain such as medulla, pons and midbrain). Damage to these areas can create a misalignment (or a skew) which can be defined as hypertropia.
Brainstem. Stroke in the area of the brain called brainstem can cause misalignment of the eye (s). There are parts of brainstem that control horizontal and vertical alignment. If damaged, they can cause hypo (one eye lower)- or hyper (one eye higher)- tropia.
What is the possibility of death when you have brain damage to the left side of your brain after a hemorrhage stroke?
Relative term. It depends on location and size and many many other factors.