I was diagnosed with a minimal umbilical hernia. Can this heal without surgery?

Usually not. An umbilical hernia in adults may change in size, but it almost never goes away without surgery. The surgery is very common, and you should be able to go home the same day.
Usually no. Small babies and newborns have umbilical hernias, and those will heal without intervention. After the age of 2, that percentage goes down substantially, and by 5 years old, the odds are around zero. If it's really small, and you're past child rearing years or a guy, you'll probably be fine, just keep an eye on it, otherwise it could get worse over time if stretched or strained.
No. A hernia like yours is a weakness in the abdominal wall. Although it may increase or decrease in size with weight gain or weight loss, it will never completely close. That being said, it doesn't require that you have surgery to "repair" it. Almost everybody has a natural defect at their umbilicus, but we only treat them when they are symptomatic. It sounds as though yours is in that category.