Now, there are rumors that a big earthquake will occur on July 5th , causing devastating damage in Japan. Now, there are rumors that a big earthquake will occur on July 5th, causing devastating damage in Japan.

Now, tThere are rumors that a big earthquake will occur on July 5th , causing devastating damage in Japan. There are rumors that a big earthquake will occur on July 5th causing devastating damage in Japan.

The "now" isn't really necessary. If you wanted to say "now", then can say "Rumors have started that a big earthquake......"

Now, tThere are rumors that a bigmajor earthquake will occurhappen in Japan on July 5th , causing devastating damage in Japan. There are rumors that a major earthquake will happen in Japan on July 5, causing devastating damage.

Starting with “Now” isn’t necessary and can feel a bit awkward. “Big” is very casual, so “major” sounds more serious. Also, putting “in Japan” closer to the date makes it clearer. 「Now」はなくても伝わるし、少し不自然に感じることがあります。「Big」はカジュアルすぎるので、「major」のほうが深刻さが伝わります。また、「in Japan」を日付の近くに置くと意味がはっきりします。

I think thait's ridiculous because experts claim earthquakes are impossible to predict. I think it's ridiculous because experts claim earthquakes are impossible to predict.

そうですね。

I think that'’s ridiculous because experts claimsay earthquakes are impossible tocannot be predicted. I think that’s ridiculous because experts say earthquakes cannot be predicted.

“Claim” can sound like you’re doubting experts, so “say” is softer. “Cannot be predicted” sounds clearer than “impossible to predict.” 「claim」は専門家を疑っているように聞こえるかもしれないので、「say」のほうが優しい言い方です。「cannot be predicted」のほうが「impossible to predict」よりわかりやすいです。

I think that'sCLEARER: I think such rumors are ridiculous because experts claim earthquakes are impossible to predict. CLEARER: I think such rumors are ridiculous because experts claim earthquakes are impossible to predict.

However, this rumors do has spread and create a kind ofd some fear. However, this rumor has spread and created some fear.

Or "However, this rumor is spreading and creating fear."

However, rumors do spread and create a kind ofause fear. However, rumors do spread and cause fear.

“Create a kind of fear” is a bit awkward. “Cause fear” is simple and easy to understand. 「create a kind of fear」は少し不自然なので、「cause fear」のほうが簡潔でわかりやすいです。

However, rumors doabout a July 5th quake have spread and created a kind of fear. However, rumors about a July 5th quake have spread and created a kind of fear.

COMMENT: I glanced at the manga by Ryo Tatsuki predicting this earthquake. I am 90% skeptical, but 10% of me believes. (Cf. https://www.ndtv.com/world-news/is-mangas-july-5-earthquake-prediction-going-to-come-true-what-we-know-8827497 )

Of course, I hope nothing bad happens. Of course, I hope nothing bad happens.

Of course, I hope nothing bad happens. Of course, I hope nothing bad happens.

Just add a comma after “Of course” to sound natural and correct. 「Of course」のあとにカンマを入れると、自然で正しい表現になります。

In fact, some flights from overseas to Japan have been canceled. In fact, some flights from overseas have been canceled.

Japan is implied from the previous sentence, so it's more natural without it.

In fact, some flights from overseasabroad to Japan have been canceled. In fact, some flights from abroad to Japan have been canceled.

“From abroad” sounds more natural than “from overseas.” 「from abroad」のほうが自然な響きです。

I plan to refrain from unnecessary outings on that day unless it is not an emergency. I plan to refrain from unnecessary outings on that day unless it is an emergency.

I plan to refrain from unnecessary outings on that day unless it is not an emergency.Unless it's an emergency, I plan to avoid going out on that day. Unless it's an emergency, I plan to avoid going out on that day.

Rewrote so it sounds more natural (to me). If you mean you must go out then "is an" is better. 緊急だったら、行く。

I plan to refrain fromavoid unnecessary outings on that day unless it is not an emergency. I plan to avoid unnecessary outings that day unless it is an emergency.

“Refrain from” sounds formal; “avoid” is more natural in everyday talk. Also, “unless it is not an emergency” is confusing because of the double negative — better to say “unless it is an emergency.” 「refrain from」は堅苦しいので、「avoid」のほうが自然です。また、「unless it is not an emergency」は否定が二重になっていてわかりにくいので、「unless it is an emergency」が正しいです。