Would fate be a theme or a subject. Most websites would just list fate as a theme. However, i learned before that a subject is what a book talks about and a theme is like a lesson. So what would fate be?

Answer 1

Fate itself is simply a topic or an angle for the playwright or the storyteller or the novelist.

Read through the themes listed and explained on this webpage:
http://www.sparknotes.com/shakespeare/romeojuliet/themes.html
Do you see how themes are usually stated in phrases or clauses?

You're right in thinking that themes are often the lesson (or a lesson) that the author wants his/her readers or audience to "get" by means of the story.