Here are the sentences with the specified modal verbs filled in:

2. I advise you not to drink beer. (should)
- You shouldn't drink beer.

3. Would you mind telling me the way to the city post office? (SHOW)
- Could you tell me the way to the city post office?

4. Is there a lake in the park?
- Does there is a lake in the park?

5. The picture is on the wall.
- There is the picture on the wall.

6. Jazz is her favorite kind of music.
- She likes jazz most.

7. I am not happy when children lie to their parents.
- Children shouldn't lie to their parents.

8. It's good if you say "Thank you" to a person who has helped you.
- You should say "Thank you" to a person who has helped you.

9. It is not good to stay up so late to listen to music.
- You shouldn't stay up so late to listen to music.

10. It is essential that you do your homework before going to school.
- You must do your homework before going to school.