Why do we put THE before "Far East" but we don't put THE before "South East Asia" but both are the names of parts of Asia? Looking forward to your answers!
"Asia" is a proper noun, i.e. a name so does not require the definite article ("the"). "East Asia" is a proper noun modified by an adjective so does not require the article. "East" is not a proper noun, it is an adjective, but we can turn it into a noun using the article: "The East", i.e. places which are East; much like you can with other adjectives - compare "blessed are the meek", i.e. blessed are the people who are meek.
J.R. has posted helpful links in a comment above, which you might find useful if you want to explore more.
"The" appears in country names when the noun is a general term with a kind of adjective before, as in the Netherlands (low-lying lands), the United States, the Philippines (Philippine islands). Often with rivers as the Nile, the Mississippi. But there is no regular system in geographical names and grammars have a whole chapter on this topic.