It is a myth that the brain quits generating new cells once you reach adulthood. They are regenerating all the time.
Ice cream headache or brain freeze is a temporary pain due to eating or drinking a cold substance or when exposed to cold air. The shooting pain lasts for a few seconds and does not require treatment.
An active brain can certainly help in improving memory by strengthening the connections between neural impulses in brain.
Do you want to sharpen the way your brain works? Try writing by hand to sharpen your mind and increase your focus.