Here are the correct answers for each of the sentences along with brief explanations:

1. In recent years, there has been **many** interest in sustainable living and eco-friendly products.
- **Correct Answer:** *many*
**Explanation:** The uncountable noun "interest" is often perceived in an uncountable context, but in common usage, the phrase "there has been many" can sound awkward. The better phrasing would be "a lot of" or "much".

2. *The Great Gatsby* **which** was published in 1925, remains a classic in American literature.
- **Correct Answer:** *which*
**Explanation:** "Which" is used to introduce a non-defining relative clause providing additional information about "The Great Gatsby."

3. If they **use** the budget more carefully this year, they **will have** fewer money problems next year.
- **Correct Answer:** *use/will have*
**Explanation:** This sentence is a conditional sentence (first conditional) that talks about a real future situation.

4. Running every day is **better** than running once a week for keeping fit.
- **Correct Answer:** *better*
**Explanation:** "Better" is the comparative form used to compare two things, indicating that running every day is a superior option.

5. While she **was writing** the letter, her brother was playing video games in the next room.
- **Correct Answer:** *was writing*
**Explanation:** The past continuous tense "was writing" indicates an action that was ongoing at a specific time in the past.

6. Tuan: "I just started working at a new café downtown!" Mai: “**That sounds exciting! Congratulations!**”
- **Correct Answer:** *That sounds exciting! Congratulations!*
**Explanation:** This response is appropriate as it acknowledges Tuan's news positively.

7. While they **were watching** a movie in the living room, their neighbors suddenly knocked on the door.
- **Correct Answer:** *were watching*
**Explanation:** The past continuous "were watching" indicates that the action was ongoing when another action (knocking) occurred.

8. By the time the concert started, they **had been standing** for over two hours in line, waiting for their tickets to be checked.
- **Correct Answer:** *had been standing*
**Explanation:** The past perfect continuous "had been standing" indicates an action that was ongoing up until another event in the past.

9. According to Minh, participating in a team sport is **more challenging** than playing an individual sport because it requires more cooperation and communication.
- **Correct Answer:** *more challenging*
**Explanation:** "More challenging" is the correct comparative form used to compare the levels of challenge between team and individual sports.

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