Here are the corrections for the multiple-choice questions you provided, along with explanations:

### Corrections
1. **Question 27**: The letter **A** should be corrected.
- **Correction**: "My brother and I like lying on the beach."
- **Explanation**: The phrase "I and my brother" is not correct in English; it should be "My brother and I" to maintain proper subject order.

2. **Question 28**: The letter **B** should be corrected.
- **Correction**: "Nam is far from (C) his family so he remembers (A) his parents in his hometown so much."
- **Explanation**: "Far from" indicates distance, which fits better with "misses," but if correcting, we might keep "his family" as it doesn't require change.

3. **Question 29**: No correction is necessary.
- **Explanation**: The sentence is correctly structured and clear about parents teaching their children.

### True/False Sentences
1. **Sentence 30**: True
- **Explanation**: A hobby is indeed often associated with free time as it’s a form of leisure activity.

2. **Sentence 31**: True
- **Explanation**: People can gain skills and knowledge from engaging in hobbies as they often involve learning and practice.

3. **Sentence 32**: False
- **Correction for context**: Hobbies can be developed at any age, not just from ages two to three.

4. **Sentence 33**: True
- **Explanation**: It is generally difficult to predict one’s new hobby development as interests change over time.

5. **Sentence 34**: True
- **Explanation**: Involvement in hobbies can positively or negatively affect health, depending on the nature of the hobby.

### Vocabulary Context
- **Playing board games**: Option A is a clear and true statement.
- **Interest**: Option D aligns with being an interesting hobby because it encourages strategic thinking.

If you have any further questions or need additional clarification, feel free to ask!