1, 2 and 3 are correct. 4 could use the definite or the indefinite article (or none with the plural), depending on the meaning.
She reads a Keyhan newspaper.
She reads the Keyhan newspaper.
She reads Keyhan newspapers.
You must capitalise English because it is a proper noun.
Edit: I assumed "Keyhan" was a language! Is it the name of a newspaper? If so, then it depends on what the newspaper is called. If it's official name is "The Keyhan", then you must capitalise "The". If it's just called "Keyhan" then I would simply say "She reads Keyhan [every day]".