1. The circle was missing a piece.

2. A piece was not in the circle.
3. A piece was missing from the circle.

(Does #1 mean #2 or #3?)

4. Think of the after story of the missing piece. On the way the circle met an oval. The oval said, " You look ugly. You have a round face and you are missing a piece. I have an over face. A good-looking person has an oval face."
Because of the oval, the circle felt sad. However, worms, butterflies and bugs said to the oval, "Appearance is not very important. Personality is much more important than appearance.
And because of shortcomings, we can become better and better in the future. We like the circle that has a missing piece." So, the oval said, "I'm sorry. You are right." They became friends and shook hands with one another/each other. They played together sining songs.

(Would you like to check the passage? Correct the errors,please. Thank you. Do I have to use 'each other' or 'one another'?)

Yes, all of the first three mean the same and are correct.

I have an oval face . . .

The rest of the passage is perfect.

This is better: ". . . shook hands with each other."

Based on the given context, phrase #1 "The circle was missing a piece" can be understood as both #2 "A piece was not in the circle" and #3 "A piece was missing from the circle." These phrases are all conveying the same meaning that there is a piece that is not present in the circle.

Regarding the passage, here is the corrected version:

"Think of the aftermath of the missing piece. On its journey, the circle encounters an oval. The oval tells the circle, 'You look ugly. Your face is round, and you are missing a piece. I have an oval face. A good-looking person has an oval face.' Hearing this, the circle feels sad.

However, worms, butterflies, and bugs respond to the oval, saying, 'Appearance is not very important. Personality is much more important than appearance. And through our shortcomings, we can grow and improve in the future. We admire the circle even with the missing piece.' In light of this, the oval admits, 'I'm sorry. You are right.'

They become friends and shake hands with each other. They play together, singing songs."

As for your question about using "each other" or "one another," both phrases can be used interchangeably in this context since they refer to the friendship and interaction between the circle and the oval.