First of all you try to create two primary keys (author and id) which is impossible.
Furthermore values in VARCHAR columns are variable-length strings - but you have to define a maximum length for VARCHARs, e.g.:
author VARCHAR(50). That means AUTHOR-values can not exceed 50 characters. A VARCHAR can have any length between 1 and 255 characters.
So your correct SQL-Query could look like this:
CREATE TABLE news (author VARCHAR(50) NOT NULL, date DATE NOT NULL, id INT NOT NULL AUTO_INCREMENT,
message TEXT NOT NULL, title VARCHAR(50) NOT NULL, PRIMARY KEY (author), INDEX (author, id),
UNIQUE (id)) ;
Hope this helps you.