1. They made a pose like a model.

2. They made poses like models.
*2-1. They made poses like a model.
*2-2. They made a pose like models.

3. They made a mistake.
4. They made mistakes.

5. They made a card for Mom.
6. They made cards Mom.
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(Can we use all the expressions above? I have written down explanations for each sentence above as follows? Are my explanations plausible?)

1. They made only one pose. All of them made one pose like their favorite model.

2. They made their own poses. Their poses were different.

3. They made only one mistake. They were working together.

4. They made various mistakes.
Each of them made mistakes.

5. They made only one card for Mom.

6. Each of them made a card for Mom.
They made several cards.

3 answers

Rather than saying/writing "made a pose" you need to simply use the verb form: they posed.

3, 4, 5, and 6 are fine, and so are your explanations for them.
1. They made a pose like a model.
2. They made poses like models.
*2-1. They made poses like a model.
*2-2. They made a pose like models.

3. They made a mistake.
4. They made mistakes.

5. They made a card for Mom.
6. They made cards for Mom.
They posed like models.

3 - 6 are fine.