What age do children begin writing?
Whenever they feel like it.
Usually when they start to have interests in writing, grammar, reading, and anything to do with writing or books. They might start off with good ideas and write them down in short paragraphs. Personally, I daydream a lot about stories and work on them from time to time. That's all for serious writing as in stories.
Kids start actually learning to write at preschool. They are taught to write their names. So technically at around 4 or 3 years old.