Is good writing an indicator that the person is a good listener and a good reader?

Not necessary. Writing is one way of expressing one's most profound emotions and/or feelings. A writer doesn't necessarily have to be completely literate. There are many famous authors and poets who never even graduated from college; for instance, Mark Twain or Maya Angelou. They are considered autodidacts. Another famous autodidact is Helen Beatrix Potter. She's knowing for stating, "Thank goodness I was never sent to school; it would have rubbed off some of my originality".

I, personally, don't think a good writer is required to be either a good listener and/or a good reader. We live, breathe and write what see- the ever-changing world around us. My favourite quote is by James A. Michener, "I love writing. I love the swirl and swing of words as they tangle with human emotion".

Its not really necessary but it indicates the persons creativity nature somewhere inside.The person with good handwriting is smart indeed to understand things in a better as well as more possible ways. Good handwriting individuals are very good at designing works in fact any kind of thoughtful of works.