"My dear" is usually for people who are closer. It is a term of endearment - someone who is dear to you - though it is considered a little old-fashioned in America. Men usually don't say it to other men, but you can hear some couples saying it, and women who are friends when say it to each other. Hope that helps

The short answer is, don't use it. I only imagine older women saying this to someone they are about to give advice to. As an exclamation that you might say if you drop a plate, or spill wine, or if someone cut's their finger, you might say, "Oh, dear." It has the same affect as かわいそう. "Dear" is an affectionate term. I'm not sure how to translate it. But generally, the only time you will use the word "dear" is when you begin a letter. ("Dear Alice, I'm glad you asked this question.")