TIn my opinion, the Lantern Festival, in my opinion, is the formal ending of the Chinese New Year.

This reads smoother than before.

Usually, aAfter the first day of the new year, people mainly visit their relatives, and don't do ousually don't do anything other than visiting their thingrelatives until after the Lantern Festival.

Another correction to make things read smoother. The word 'mainly' was dropped because the word 'usually' already carries the same meaning.

(the fifteenth day of the new year).

Its just awkward and superfluous to include this in brackets here. If you want to indicate the lantern festival is on the 15th day of the year, its better to directly combine it with the previous sentence. For example,

"After the new year begins, people usually don't do anything other than visiting their relatives until after the fifteenth day of the year: the Lantern Festival."

To prevent "day of the year" from appearing twice, the "first day of the year" is reworded. But this creates another subtle tone problem. This sentence's structure introduces "Lantern Festival" as though it hasn't been mentioned before. But the first sentence does mention the Lantern Festival already, so now the second corrected sentence sounds awkward. An easy way to fix this would be to swap the order of these sentences, so the beginning of your text now says

"After the new year begins, people usually don't do anything other than visiting their relatives until after the fifteenth day of the year: the Lantern Festival. In my opinion, it is the formal end of the Chinese New Year."

Now the awkward feeling is gone, and the second mention of "Lantern Festival" was changed to "it is" to prevent it from appearing twice. English is very annoying like this, where adding just one more piece of meaning to a sentence forces you to move everything around it.

Children carry lanterns while going around the villages to collect some unexploded firecrackers they find.

"Villages" is plural, but not using the word "the" in front of it makes it sound awkward in this context.

This scene tookwould take place in the countryside decades ago, when I was a kid.

Comma added to match reading cadence of this kind of sentence.

Where tThere was no electricity or any entertainment. back then.

The lantern was made of wooden materials and paper.

After the Lantern Festival, everyone thinks that the new year isthe new year is considered to be completely gone.

Usually, after the first day of the new year, people mainly visit their relatives, and dwon't do other things until after the Lantern Festival. (Lantern Festival is the 15th day of the new year)

(the fifteenth day of the new year).

Children carry lanterns while going around villages to collect some unexploded firecrackers.

Wheren there was no electricity or any entertainment.

A candle was put oin the center of the lantern's bottom, so the lantern easily gets burned when children carry it around.