I just subscribed to the Disney Plus membership for one year.

You want to use past tense here since you've just done this.

In Korea, it started to service sincthe service became available yesterday, and many Koreans are subscribing.

It's more natural to say, "the service became available yesterday" or "it's been available since yesterday."

My children really like to see Disney and Pixar charactoers, that's why I subscribed to the service.

In English, we say we "subscribe to" something.

On the service, I noticed that Marvael and National Geographic contents are there.

Again, you want to make sure to use past tense.

I think, my family will be falling into the ocean of the contents.

Grammatically, it's natural to say "to be doing x." The past participle is important.

I just subscribed to the Disney Plus membership for one year.

In Korea, it started tothe service sincetarted yesterday, and many Koreans are subscribing.

My children really like to see Disney and Pixar charactoers, that's why I subscribed to the service.

On the service, I noticed that Marval and National Geographic contents are theravailable.

I think, my family will be fall into the ocean of the contents.

I just subscribe theo Disney Plus membership for one year.

You can also refer to Disney Plus as Disney+

Subscribe to ~~~

In Korea, it started to service sincepremiered yesterday, and many Koreans are subscribing.

Premiered - 초연

If you use many make sure what comes after it is plural

My children really like to see Disney and Pixar charactoers, that's why I subscribed to the service.

On the serviceDisney+, I notice that Marvael and National Geographic contents are on there.

It would be better to use their branding instead of repeating service

I think, my family will be falldrown in the ocean of the contents.