#3a - comma after "writer". Otherwise, all perfect are perfect and have perfect grammar.
The structure (in all six sentences) that places the profession "writer" is directly next to the name of a person is called "apposition". It is correct, and commonly used.
Both sentences labeled #2 are correct in spite of the absence of an article. In both, the basic sentence is
" This book was written by Neil Gaiman"
which requires no article. When you add "famous English writer", no article is needed because apposition works without the addition of articles.