Here are the correct answers along with detailed explanations for each one:

1. **I would live to by **sea**
- **Answer**: **b. an**
- **Explanation**: "Live by sea" is a common phrase, referring to living near the ocean or a large body of water. "The sea" can also be correct, but if you're referring generally to the concept of "sea," "an" can imply the idea of being alongside any sea, which is acceptable in this context.

2. **Harry is a sailor. He spends most of his life at **sea**.
- **Answer**: **b. an**
- **Explanation**: Similar to question 1, when saying he spends his life "at sea," it refers to being out in the ocean. “At sea” is a set phrase that doesn't require an article.

3. **There are billions of stars in **space**.
- **Answer**: **c. the**
- **Explanation**: "The space" refers to the universe in general where all stars exist. In this context, "space" does typically allow for the definite article "the."

4. **He tried to park his car but **space** wasn't big enough.
- **Answer**: **a. the**
- **Explanation**: "The space" refers to a specific parking space that he is trying to use, indicating a particular area that is known in the context.

5. **We often watch **television**.
- **Answer**: **d. φ** (no article needed)
- **Explanation**: When talking about "television" in a general sense (as a medium), no article is needed. We often watch television as a concept.

6. **Can you turn off **television**, please?
- **Answer**: **a. the**
- **Explanation**: In this context, "the television" refers to a specific device that the listener has, thus the definite article "the" is appropriate.

7. **We had **dinner** in a restaurant.
- **Answer**: **d. the**
- **Explanation**: When saying "had dinner," it's common to use no article because dinner is considered a meal in general terms.

8. **We had **a meal** in a restaurant.
- **Answer**: **b. an**
- **Explanation**: This is an indefinite reference to one of many possible meals. "A meal" indicates we had one meal among many options.

9. **Thank you. That was **a** very nice lunch.
- **Answer**: **a. a**
- **Explanation**: "A very nice lunch" indicates that it was one instance of lunch among many possible lunches, hence the indefinite article "a" is appropriate.

10. **Where can **people** buy everything they need?
- **Answer**: **d. no article**
- **Explanation**: "People" refers to humans in general, making it a plural noun that does not require an article.

11. **Her parents are now working in **Europe**.
- **Answer**: **d. no article**
- **Explanation**: When referring to continents or countries in general, no article is required.

12. **He majors **in** English.
- **Answer**: **b. a**
- **Explanation**: "Majors in English" means he studies that subject, where an article isn’t usually necessary.

13. **Mark Twain**, **an** American writer, wrote "Life on the Mississippi River".
- **Answer**: **b. an**
- **Explanation**: Since "American writer" introduces Mark Twain as one of many, the indefinite article "an" is fitting.

This should provide a comprehensive understanding of the grammatical choices for each sentence.