Middle Ages: Avicenna, and if you want to include them, One Thousand and One Nights.
Modern Times: What Jacktheguy said. Also, Haruki Murakami, Khaled Hosseini, Kazuo Ishiguro, and many more.
The prosperity and global dominance of Europe/North America explain why it was easier for white people to attain the necessary education and leisure time to produce literature.
Things of the past like slavery and more pervasive racism may explain why it used to be extremely difficult if not impossible for notable non-white authors to emerge in Europe/North America until rather recently. It's not as if American slaves had written works of the same literary magnitude as War and Peace, and now white people refuse to acknowledge their achievements.
White people live predominantly in North America/Europe. This means that they are better equipped at understanding literature from these continents - hence the better representation of African Americans. Black American authors are much better understood by fellow Americans than Black Nigerians. Should it be surprising that people from vastly different regions, with different environments, religions, histories and so forth, do not form one kind of balanced literary canon? It would be a Herculean task for any culture (or whatever it is you file "White people" under) to even approximately represent the works of other cultures in their canon. And I wonder if any "culture" in history besides the current "White" one has ever stressed diversity so much as a value in itself.
Would also be nice if people stopped overestimating the importance of imperialism and trying to blame it for everything.
As for the questions on 'To Kill A Mockingbird', 'Romeo and Juliet', and '1984', I read those books so long ago I just could not remember those details.