Those were you tiny mistakes. Keep practicing!!

Please excuse me for piling on, I do it with the best intentions.

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The title should be: 

>> Describe a newspaper or magazine you enjoy reading".

>> I can read it anywhere at any time, because I use my iPhone to check the news. 

"Anywhere" is a bit better than "everywhere" here, because you want to say that you are able to read in any place, not that you actually do read in all the places in the universe. The same logic applies to every time / any time. It's like the difference between 何時も and 何時でも.

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Further on: 

 I think news articles are often written by one person and many articles are just his are only a matter of opinion not objective. Of course, news apps are said convey the same personal opinions, but there are many articles in the same cases on the same topics. So we can see a lot of variety of thinking on the internet. Moreover, we can use these apps for free and see the latest articles.

I always read about baseball games, football games and the economy on it online. We need to know these the news as fast quickly as we can, because these news are renewing at all times it is constantly being updated. That's why I always use news apps to read news, and I buy sports magazine to enjoy it once a month. Thank you!

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Quickly vs. fast: "we need to know as fast as we can" sounds like we are the ones who need to go fast. But actually, we want the news media to go fast, not ourselves. "As quickly as possible" = arriving as soon as possible, with the minimum possible delay.