Here’s the evaluation of the sentences regarding the omission of the relative pronouns, along with the rewritten versions where possible:

1. **You know the boy who broke the windows last night?**
- **Omission:** Yes
- **Rewritten:** You know the boy **(who)** broke the windows last night?

2. **The students who were punished by the teacher are lazy.**
- **Omission:** Yes
- **Rewritten:** The students **(who)** were punished by the teacher are lazy.

3. **The house that is being built now belongs to Mr. Pike.**
- **Omission:** Yes
- **Rewritten:** The house **(that)** is being built now belongs to Mr. Pike.

4. **There is a good restaurant where we can eat good food.**
- **Omission:** No
- **Rewritten:** There is a good restaurant where we can eat good food.

5. **That is the hotel where we can stay.**
- **Omission:** No
- **Rewritten:** That is the hotel where we can stay.

6. **Here is the form that you must fill in.**
- **Omission:** Yes
- **Rewritten:** Here is the form **(that)** you must fill in.

7. **We visited Barcelona, which is a city in northern Spain.**
- **Omission:** No
- **Rewritten:** We visited Barcelona, which is a city in northern Spain.

8. **The boy who are flirting you is my ex-boyfriend.**
- **Omission:** Yes
- **Rewritten:** The boy **(who)** is flirting with you is my ex-boyfriend.

9. **The smartphone that costs £200 is very good.**
- **Omission:** Yes
- **Rewritten:** The smartphone **(that)** costs £200 is very good.

10. **Mrs. Smith, who is very smart, lives on the fourth floor.**
- **Omission:** No
- **Rewritten:** Mrs. Smith, who is very smart, lives on the fourth floor.

11. **This is the car that John bought at an auction.**
- **Omission:** Yes
- **Rewritten:** This is the car **(that)** John bought at an auction.

12. **My colleague with whom I'm doing the project should be here as soon as possible.**
- **Omission:** No
- **Rewritten:** My colleague with whom I'm doing the project should be here as soon as possible.

13. **That’s the woman whose house has been broken into.**
- **Omission:** No
- **Rewritten:** That’s the woman whose house has been broken into.

Feel free to ask if you need more help!