I watched a movie at the cinema with my daughter today.

"cinema" requires an article, which should be "the" here.

Today is a national holiday in Japan, so I could go to athe theatre.

Note that "theatre" is a British spelling of "theater". It's not incorrect, but worth being aware of.

The movie iwas for kids, thenand it was simple and peaceful story.

"Sumikko Gurashi" means someone who lives in a corner.

Quotation marks make it clear what you're explaining here.

It’s a famous contentfranchise in Japan.

"series" would also work

They are cute and characteristicful.

"characteristic" is used to refer to something that defines the character of something else. For example: "Simple stories are characteristic of children's movies".

"characterful" refers to something that has a lot of personality and charm, which I think is what you were going for here.

The story of the movie was interesting but common thingsit was a bit mundane.

I'm not entirely sure what you mean by "common things" here so taking a guess. "mundane" is used to refer to things that are dull or plain

Many characters cooperated with each other to solve problems, and there was no villain.

In spite of a little bit lack ofit not being very thrilling, my daughter enjoyed this movie.

Reworded to be more natural.

We took aate lunch after the movie, and bought her clothes for wintersome winter clothes.

"took" isn't used in relation to meals - we would generally say either "had" or "ate".

The weather report said weit will getbe 5 degrees at tomorrow morning.

It is becomgetting really cold.

Your original sentence makes sense and isn't incorrect, but I think "getting" is a very natural way of phrasing this

We should take care ofor our health.

"of" is a more natural word choice here

I watched a movie at the cinema with my daughter today.

Today is a national holiday in Japan, so I could go to a theatrer.

I write in American English, so I use the "theater" spelling. "Theatre" is the proper spelling in British English.

The movie iwas for kids, then i. It was a simple and peaceful story.

We watched the Sumikko Gurashi’s movie.

"Sumikko Gurashi" means someone who lives in a corner.

It’s a famous contentfranchise in Japan.

They are cute and characteristic.

Uh… I am actually not sure what you intended to say here, but I don't think "characteristic" was the word you intended.

The story of the movie was interesting babout common things, but it was still interesting.

Many characters cooperated with each other to solve problems, and there was no villain.

In spite of a slittle bight lack of thrill, my daughter enjoyed this movie.

We took aate lunch after the movie, and bought her clothes for winter.

The weather report said that we will get 5 degrees atby tomorrow morning.

We should take care ofor our health.

The movie is for kids, then it was simple and peaceful story.

The "then" is unnecessary

It’s a famous content in Japan.

Content seems too broad, so I don't know what it refers to.

They are cute and characteristic.

Characteristic refers to a certain quality but it is not a quality itself

So what characteristic/quality are you referring to?

The story of the movie was interesting but common things about regular things like life in college.

Common things is not used well, it leads to tell what the common or usual things are but it doesn't tell us about them.

In spite of a little bit lack of thrill, my daughter enjoyed this movie.

We took a lunch after the movie, and bought her clothes for winter.