I would like to improve my writing skills because ı am quite bad about that it. I would like to improve my writing because ı am quite bad at it.

You could also say, "I would like to improve my writing skills because they are quite bad."

In the future, ı want to be writer who writes about short story. In the future, ı want to be writer who writes a short story.

Yes ı am not sure how may ıI can improve myself, but ı am sure that, firstly, ı should start to write. Yes ı am not sure how I can improve, but ı am sure that, firstly, ı should start to write.