1. You can't expect to preserve the man-made wonders without taking action.
- Explanation: In this sentence, the verb "preserve" is in its base form. To make it grammatically correct, you need to use the infinitive form "to preserve". So the correct form is "expect to preserve".

2. She's a good manager because she never avoids dealing with the problems of her staff.
- Explanation: The verb "deal" requires the gerund form in this sentence. So the correct form is "avoids dealing".

3. Would you mind telling me about the French Gothic architecture?
- Explanation: The verb "tell" is in the correct form here, as it is already in the base form and matches the sentence structure.

4. I imagine going back to the 20th century and witnessing the construction of Cu Chi Tunnels.
- Explanation: The verbs "go" and "witness" are in their base forms, which are correct for this sentence structure.

5. We recommend booking early, as this is a popular event.
- Explanation: The verb "book" is in the correct form here, as it matches the sentence structure and conveys the intended meaning.

6. Youngsters nowadays seem to lack awareness of protecting the public places.
- Explanation: The verb "lack" requires the infinitive form in this sentence. So the correct form is "seem to lack".

7. A lot of small towns in the area are definitely worth visiting.
- Explanation: The verb "visit" is in the correct form here, as it matches the sentence structure and conveys the intended meaning.

8. E-mail allows us to send messages all around the world quickly and easily.
- Explanation: The verb "send" is in the correct form here, as it matches the sentence structure and conveys the intended meaning.

9. I suggested putting the matter of restoring Ben Thanh Market to the committee.
- Explanation: The verb "put" is in the correct form here, as it matches the sentence structure and conveys the intended meaning.

10. On the way to Hue, we stopped to pay a visit to a relative in Da Nang.
- Explanation: The verb "pay" requires the infinitive form in this sentence. So the correct form is "stopped to pay".