Here are the identified errors along with corrections for each sentence:

1. **Sentence:** Apples are being **wash** in the yard by my mother at the present.
**Error:** B (wash)
**Correction:** washed
**Corrected Sentence:** Apples are being **washed** in the yard by my mother at the present.

2. **Sentence:** We **will going** to spend our summer holiday in Da Lat next month.
**Error:** A (will going)
**Correction:** are going
**Corrected Sentence:** We **are going** to spend our summer holiday in Da Lat next month.

3. **Sentence:** He is encouraged to take part in his school's **culture** activities.
**Error:** C (culture)
**Correction:** cultural
**Corrected Sentence:** He is encouraged to take part in his school's **cultural** activities.

4. **Sentence:** We have a small party in **one of our teacher's** houses tomorrow evening.
**Error:** B (one of our teacher's)
**Correction:** one of our teachers'
**Corrected Sentence:** We have a small party in **one of our teachers'** houses tomorrow evening.

5. **Sentence:** The refrigerator **is going to be** repaired by Mr. Pike at the moment.
**Error:** B (is going to be)
**Correction:** is being
**Corrected Sentence:** The refrigerator **is being** repaired by Mr. Pike at the moment.

### Summary of Errors:
1. B - wash → washed
2. A - will going → are going
3. C - culture → cultural
4. B - one of our teacher's → one of our teachers'
5. B - is going to be → is being