AreIs there any particular news that you were following? Is there any particular news that you were following?

News is actually singular even though it has an "s".

AreIs there any particular news that you weare following? Is there any particular news that you are following?

If you are still following it now, then it should be in the present tense as above. If you are just talking about a news story that you were following in the past but don't really follow now, then you could say something like "Have there been any particular news stories that you followed in the past?".

AreIs there any particular news topic that you weare following? Is there a particular news topic that you are following?

You mixed up present and past tenses in the title.

AreIs there any particular news that you weare following? Is there any particular news that you are following?

Are there any particular news that you werestories you’ve been following? Are there any particular news stories you’ve been following?

There have been too many earthquakes in Japan in recent years. There have been many earthquakes in Japan in recent years.

Scientists often say that thea big earthquake will be occurred under the city of Tokyo within 10 years. Scientists often say that a big earthquake will occur under the city of Tokyo within 10 years.

I think I understand why you choose to use "the" here since there is one particularly big one that is being referred to. But since it hasn't occurred yet, it is still regarded as an unknown earth quake and using "a" is more natural here. Though you may put quotes around it to emphasize the particular one being predicted: Scientists often say that "The Big Earthquake" will occur under the city of Tokyo within 10 years.

Scientists often say that thea big earthquake will be occurred under the city of Tokyo within 10 years. Scientists often say that a big earthquake will occur under the city of Tokyo within 10 years.

Maybe a more natural way to say this is "Scientists often say that there will be a big earthquake in Tokyo within (the next) 10 years", although the correction above is also perfectly fine.

Scientists often say that the big earthquake will be occurred under the city of Tokyo within 10 years. Scientists often say that the big earthquake will occur under the city of Tokyo within 10 years.

"Will occur" is future tense whereas "will be occurred" mixes future and past to result in a confused reader.

Scientists often say that the big earthquake will be occurred under the city of Tokyo within 10 years. Scientists often say that the big earthquake will occur under the city of Tokyo within 10 years.

Scientists often say that the biga major earthquake will becould occurred under the city of Tokyo within 10the next ten years. Scientists often say that a major earthquake could occur under Tokyo within the next ten years.

My work office is in Tokyo, so I’m very afraid of that. My work office is in Tokyo so I’m very afraid of that.

My work office is in Tokyo, so I’m very afraid of that. My office is in Tokyo, so I’m very afraid of that.

We cawon’t be able to handle thea national disaster like that. We won’t be able to handle a national disaster like that.

"We won't be able to handle such a disaster" and "we won't be able to handle a disaster on that scale" are equally valid alternatives. Since you're talking about a future event, I think "can't" should be changed to "won't be able to".

We can’t handle thea national disaster. We can’t handle a national disaster.

We can’t handle the nationnot fully prepare for or control a natural disaster. We cannot fully prepare for or control a natural disaster.