Here are the mistakes identified and corrected for each sentence from the provided text:

2. **Mistake:** "this hand-embroidered picture was very expensive"
**Correction:** "this hand-embroidered picture **is** very expensive" (Option A)

3. **Mistake:** "but he studies very well"
**Correction:** "but he studies very **hard**" (Option C)

34. **Mistake:** "In spite of my father is old"
**Correction:** "In spite of my father **being** old" (No option available)

35. **Mistake:** "In spite the danger"
**Correction:** "In spite **of** the danger" (Option A)

36. **Mistake:** "Although Nam worked very hard, but he didn't pass"
**Correction:** "Although Nam worked very hard, he didn't pass" (Remove "but")

37. **Mistake:** "because her old age"
**Correction:** "because of her old age" (Option A)

38. **Mistake:** "John didn't go to work because of he was seriously ill"
**Correction:** "because **of** he was seriously ill" (Replace “of” with "that" for better structure, typically "because he was seriously ill." No option available)

39. **Mistake:** "due to he worked hard and logically"
**Correction:** "due to his working hard and logically" or "because he worked hard and logically." No option available.

40. **Mistake:** "The plane couldn't take off since the bad weather"
**Correction:** "because of the bad weather" (Option D)

41. **Mistake:** "number of visitors dropped quick"
**Correction:** "number of visitors dropped **quickly**" (Option D)

42. **Mistake:** "a new hospital is being build"
**Correction:** "a new hospital is being **built**" (Option D)

Let me know if you need further assistance!