Help Second Newspaper Translation

Close but not correct. 町 is town, village is 村, and city as an administrative section/district is 市.
Also note that 町 refers to two different administrative section/district; 〇〇郡××町 (e.g. 鳥取県岩美郡岩美町, 鳥取県八頭郡智頭町)
and 〇〇市××町 (e.g. 鳥取県鳥取市東町, 鳥取県鳥取市相生町). The translation is "town" in both cases anyway, though.

My dictionary doesn't seem to distinguish town from village. It provides four different translations namely: town, village, block or street.

I googled the difference between a village and a town:
"A village is a small settlement usually found in a rural setting. It is generally larger than a "hamlet" but smaller than a "town". Some geographers specifically define a village as having between 500 and 2,500 inhabitants. In most parts of the world, villages are settlements of people clustered around a central point."

I then checked the population of Iwami, about 11,000 人 according to Google. So it is indeed a town according to that definition. So I'm not sure as to why my dictionary app conflates village and town in Japanese. Jisho doesn't identify 町 as a village so maybe I should change my dictionary app for a different one which is more nuanced in its definitions.

The population changes. It's named when it's founded, but even if the population increased or decreased, the name of the town/village is not changed. It's Iwami town regardless of the present population.

In the first place, you should refer to the Japanese definition of 村 , 町 and 市, not the definition of the English words village or town.


EDIT:
Here's the legal definition of 村 , 町 and 市. It's all in Japanese, but you would be able to get the gist of it using Google Translate or something.