Here are the corrections for each group, with the correct sentence identified:

1. **Correct Sentence**: John is playing chess with him.
- Correction: "Him is playing chess with John." → "He is playing chess with John."

2. **Correct Sentence**: The girls and boys are going to the concert right now.
- Correction: "The girls and boys go to the concert right now." → "The girls and boys are going to the concert right now."

3. **Correct Sentence**: Those are my dog's shoes.
- Correction: "Those are my dog's shose." → "Those are my dog's shoes."

4. **Correct Sentence**: Do you want a sandwich with your apple?
- Correction: "Do you want a sandwiches with your apple?" → "Do you want a sandwich with your apple?"

5. **Correct Sentence**: There isn't any homework today.
- Correction: "There aren't any homework today." → "There isn't any homework today."

6. **Correct Sentence**: John and Mary are cleaning their rooms at the moment.
- There is no mistake in this sentence. It is correct.

7. **Correct Sentence**: My brother and I are getting a dog today.
- Correction: "My brother and me getting a dog today." → "My brother and I are getting a dog today."

8. **Correct Sentence**: My teachers are usually happy in the morning.
- Correction: "My teacher are usually happy in the morning." → "My teachers are usually happy in the morning."

9. **Correct Sentence**: Amy doesn't like her new sneakers.
- Correction: "Amy don't like her new sneakers." → "Amy doesn't like her new sneakers."

10. **Correct Sentence**: Are there some goats and sheep on the farm?
- Correction: "Is there some goats and sheep on the farm?" → "Are there some goats and sheep on the farm?"

Let me know if you need further assistance!