English is a common language and you can use English to become an international person. First, you could get the news faster than the others could. Second, you should understand other countries for using English. Third, you would depend on English to read the latest books or magazines in the world.

Looks good to me.

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First, you could get the news faster than the others could. -> "the others" is a bit awkward because you haven't specified who you're talking about. You're just talking about other people in general rather than some particular group of other people, so I would just say "than others could".

Second, you should understand other countries for using English. -> I don't understand what this means? Do you mean that you'll be able to understand people from other countries by using English? If so, "Second, you would be able to understand people from other countries using English." would be better.

Third, you would depend on English to read the latest books or magazines in the world. -> "would depend on" almost sounds like you're being restricted to English rather than being able to use English. "Third, you could use English to read the latest books or magazines published worldwide." would sound better - "in the world" is a bit of a strange expression here.