Here are the corrections for each underlined word or phrase in the sentences:

1. **Our new car is hard to drive **than** our old car.**
**Correction:** Our new car is hard to drive **compared to** our old car.

2. **We are going to study tonight until we finish our homework.**
**Correction:** We are going to study tonight until we finish **doing** our homework.

3. **You should take a taxi although it's raining** hard.**
**Correction:** You should take a taxi **since** it's raining hard.

4. **There are a lot of food in the fridge, so help yourself.**
**Correction:** There is a lot of **food** in the fridge, so help yourself.

5. **Last weekend, my teacher took us to the** making - **car factory near our school.**
**Correction:** Last weekend, my teacher took us to the **car factory making** near our school.

6. **We are made doing all the cleaning in the house.**
**Correction:** We are **responsible for** all the cleaning in the house.

7. **Mary and her sister studied biology last year, so does Jane.**
**Correction:** Mary and her sister studied biology last year, so **did** Jane.

8. **Different kinds of newspapers** arranging in the shelves.**
**Correction:** Different kinds of newspapers **are arranging** on the shelves.

9. **Although his old age, Mark performed excellently in his latest film.**
**Correction:** Although **of** his old age, Mark performed excellently in his latest film.

10. **What happens to the grass when it is** sending **to the library?**
**Correction:** What happens to the grass when it is **sent** to the library?