Someone trying to learn English should be very cautious about what he makes of poetry and song lyrics. These often do not follow regular grammar rules and in general may use the language in unusual ways.
"As small as a world" is surely meant to be a surprising statement. We normally think of the world as very large. Note that he does not outright assert that the world is small -- he does not say, "Contrary to popular belief, the world is really rather small." Instead, he makes the statement indirectly in a comparison, as if the smallness of the world was something that everyone took for granted.
"As large as alone" is not grammatically correct because "alone" is an adverb and sometimes-adjective, while the phrase calls for a noun. But again, the writer is trying to indirectly say that the state of being alone is something very large ... whatever he means by that.