Will children too get hypoglycemia?

Sure. A number of different conditions result in hypoglycemia in children: overdose of tylenol, (acetaminophen) accidental ingestion of glucose lowering drugs or alcohol, inborn errors of metabolism, ketotic hypoglycemia, etc.
Sure. There are many causes of true hypoglycemia which can occur at any age. Neisidioblastosis is a rare condition and is more likely in children - if you suspect hypoglycemia in your child see a real pediatric endocrinologist.