The essay “What Is Happiness?”

Happiness is a very difficult category (perhaps 'concept'?), which everybody chooses for themself. We cannot describe these feelings. In my opinion, we can see it in people’s eyes. The happiness glows from inside of our soul.
Happiness glows from inside our soul (as a rule, happiness comes from the soul)
OR: The happiness glows from inside their souls (talking about the people who have it in their eyes)
For one person happiness is health, for another it is love or spirit. Some people think that happiness is only short-lived. (or 'ephemeral' for a fancy word ;) )
As a rule, we work to achieve our goal for a long time and if we are successful, we feel delight and joy. Sometimes we feel happiness when we see unbelievable scenery and beautiful buildings.
For me, happiness is my life. I enjoy every moment of it. Of course, if I go on to have a career and a family, then I will be very happy.
Just 'if I have/had' sounds like you should have a family and career now and that most people would be unhappy because of it. My suggestion hints at those things being something for the future - that will make you happy then (at the right time).
 I think that everybody can be a happy person, because everyone has relatives, and friends, and opportunities which he can realize (realiSE if you want British variant) in the future. Unfortunately, many people think they are not happy, because they have a lot of problems. We do not remember any good events and things for very long. We remember bad times and this is very typical of people. I believe that all people in the world are happy, but everyone should recall the actions in their lives, which brought them happiness.

Very philisophical - I like it! I'm not sure I could have written that much on such an elusive topic. Actually very few mistakes for such complex ideas. I hope my suggestions help but they are of course only what I think sound good. :)