the best way to answer these questions, in my opinion, is by reading them out loud and trying to "hear" the missing articles.
i Scientists are now beginning to worry about (the) contamination of (the) entire solar system.
you would need to insert two "the"s here to specify your nouns. THE contamination, meaning a specific contamination, and THE entire solar system, meaning a specific solar system.
ii People often say that (a) writer’s life is unimportant and all that matters is in books. That is usually (an) exaggeration)
you want to say "a" life, because you aren't listing a specific writer's life--just a potential writer's life. you want to say it's "an" exaggeration because it isn't THE ONLY exaggeration ever. there are many, many exaggerations, but you're only picking one--so "an."
iii In light of (the) above statement, I would like you to sign the document.
you want to insert a "the" here because you're referencing a specific statement.
