A Japanese news site introducshowed the New York Times listed the deceas of those who died from the coronavirus with their names, ages and pottedsmall biographies.

The vocabulary that was changed was because it was very uncommon.
Some small grammar errors but I think that is just because you made a long sentence :).

Describing each pottederson's biography could never happen in Japan.

BThis is because we had been strongly asked to be harmonious, that is to keep a low profile, at schools.

WatchingLooking at the New York Times site, I found it certainly simply descrbibed their biographies simply.

Loved to donwear Groucho glasses and tell jokes.

"Don" is fine in this context but be careful with it :)

As I read their simple biographies, tears naturally rolled down my face naturally.

"Tears rolled down my face naturally"
Is fine as well however it can sound more like your describing the tears movement down your face and not that it is natural to cry while reading the biographies.

The New York Times staff collectworked hard theseo collect this information.

I believe a Japanese news site wouldill describe about me someday.

A Japanese news site introducdisplayed the New York Times listed the deceased from the of those who had died of coronavirus with their names, ages and pottedsmall biographies.

I took some liberties correcting this. I changed "Listed the deceased from the coronavirus" to "list of those who had died of coronavirus" because the sentance is describing an object (the new york times list" so we need to use the noun form of list instead of the verb, and describe it using the right grammar. Hope that makes sense.

Describing each pottederson's biography could never happen in Japan.

I don't really know what you mean by "potted" biograpghy. You mean each person's?

BThis is because we had been strongly asked to be harmoniouscalm, that is to keep a low profile, at schools.

In formal English you can't start sentances with conjunctions ("and, but, because") although people do it a lot. In this case it sounds a bit too strange even for informal speech. We use tricks like starting a sentance with "this is" to make it clear that the "because" is referring to the previous sentence. Also, "harmonious" is a strange word to use in this context, something like "disciplined" or "calm" might work.

WatchingI thought the New York Times site, I found it certainly simply descrbibed their biographies very simply.

We would usually use the word "Reading" instead of "watching". I rephrased the sentance a lot to make clear that the issue you had was that the biographies were too simple. Often putting description at the end of a sentance in English shows to the reader that you are concerned about that specific element of the object you are describing. For example, "I thought the ice cream was cold" shows that you are more interested in the fact that the ice cream is "cold", rather than the fact that it is an ice cream.

About aFor example, one person;

As I read their simple biographies, tears rolled down my face naturally.

The New York Times staff collectworked hard theseo collect this information.

I believe that a Japanese news site would describe about me somedayme like this.