Possibly. The answer depends upon the area of the brain affected by the stroke; and how the blood supply to that area recovers. Best to discuss this with a neurologist; or your primary care physician.
It can. A speech therapist can be extremely helpful with this problem. See one.
Does neurogenic stuttering ever just randomly stop occurring after a stroke? Please, need some answers?
May resolve. But don't just wait. Work with a speech therapist and learn to overcome the disability.
Variable. Multiple causes of stuttering but any stroke occurring within classical speech areas can change pre-existing pattern dramatically, especially if ability to express speech is affected. So, what you ask may indeed occur subsequent to cerebral infarction.
Yes it can. Read oliver sacks, the man who mistook his wife for a hat. He describes strange cases of patients who show strange behavior following a stroke. As I recall he describes a patient who spoke more easily after a stroke. Pretty rare however.