A child may develop many fears and one such fear can be the fears of things like dogs, cockroaches, watchman, water, police, ghost and also old people. Your child may not have had a scary experience with any of these. The experience is not essentially necessary to develop fear. But these fears just develop and the child may find it difficult to overcome them. At times when we force the child against his fear he or she may overcome it but there are chances that the child may get even more frightened. With age these fears in children outgrow themselves.

You have some great tips.
I think fears can be both created from things we experience in our lifetime, or we can be born with/inherit them. I personally have found exposure to be the best form of therapy, but it really depends on the person and exposing a child to what it fears too often or too quickly may cause them to become more afraid-causing a step backward in the progress.

It really depends on the person - not every fear is outgrown and some people even carry it to their adulthood. I have met some people who have had to go to therapy in their adult years to remove certain phobias.

I think the best thing that a parent can do is just sit down with their child and talk with them. Show them that there's nothing to be afraid of. A lot of people will say that a little fear is a good thing, but that's not true at all. Children have big imaginations, and it can sometimes get the best of them, causing the fear to get out of hand.