I have been reading such kinds of papers, books and magazines as a hobby before taking the test.
---- I would write this sentence like so: As a hobby, I have been reading such kinds of papers, books, and magazines. I also read that material before taking tests.
OR
---- Before taking tests, I have been reading such kinds of papers, books, and magazines. I also read that material as a hobby.
I would not use "as a hobby" and "before taking the test" in the same sentence, with both referencing "reading such kinds of papers, books, and magazines." The way you wrote it, it sounds like you read papers as a hobby ONLY before taking the test, not as a hobby and before taking tests. I am not 100% sure on your meaning here, so my suggestion may be inaccurate.
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This is because I like reading, whether books in English or ones in Japanese.
-- Gramatically correct. It can be rewritten a few ways, but it is technically correct.
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The economist is so expensive that I only subscribe regularly to Time, in addition I read two paperbacks a month.
--The economist is so expensive that I only subscribe regularly to Time. In addition, I read two paperbacks a month.
This is two separate ideas in one sentence, and is written better as two sentences. Idea one is "the economist is so expensive"; Idea two is "i read two paperbacks a month."
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These days I read history books and non-fiction about politics more than novels.
-- These days I read history and non-fiction politics books more than novels.
History and non-fiction politics are both adjectives about books. both words describe what kind of books you are reading, so find a way to put them both before the word "books" in the sentence.