Sure, here are the correct options:

21. He barely escaped **being** pawed by the dog.
22. The authorities to postpone **closing** our beloved school.
23. She always tries to avoid **seeing** her ex-boyfriend.
24. Would you care **to come** and have a chat with me?
25. We helped her prevent **gaining** weight over the holidays.
26. I enjoy **working** with Google because they are professional.
27. I didn't mean **to hurt** your feelings. I'm really sorry.
28. She managed **to open** the door without the key.
29. Some fans can't stand **waiting** in the queue at the Apple store.
30. He missed **participating** in the campaign, but he's in luck.
31. You can save the email and finish **composing** it later.
32. She couldn't wait **to see** her son when he was born.
33. I made a suggestion but they chose **to ignore** it.
34. Would you mind **moving** your car out of the cycle lane?
35. He claimed **to be** 15, but I know he's only 12.
36. Many young people wish **to live** in the USA.
37. I never risk **going** out at night without my parents.
38. She often volunteers **to read** aloud in class.
39. In the end I gave up **trying** to persuade him.
40. The children are learning **to read** and write.