Can you please check if the following sentences are correct? Thank you.

1) “I met Mary last Monday.” (she/say)
She said that she had met Mary the previous Monday.
2) “I’m sorry, I broke the vase.” He apologized for breaking the vase.
3) “ You should really read this book, Steve! (Sally/recommend)
Sally recommended I should really read that book.
4) “ Be careful, because the roads are slippery.” (The policeman/warn/us)
The policeman warned us to be careful because the roads were slippery.
5) “I’ll help you.” (my mother/promise)
My mother promised that she would help me/to help me.
6) “We went on a school trip today!” (Peter/tell/his mother)
Peter told his mother that he had gone on a school trip that day.
7) “ I ate all the cake yesterday.” (Peter/confess to)
Peter confessed to eating all the cake the day before.
8) “I feel very well now.” (he/explain)
He explained that he felt very well then.
9) “Will your mother be at home tomorrow?” (Mary/ask/me)
Mary asked me if my mother would be at home the next day.

3) “ You should really read this book, Steve! (Sally/recommend)

Sally recommended I should really read that book.
Sally recommended that I read that book.

7) “ I ate all the cake yesterday.” (Peter/confess to)
Peter confessed to eating all the cake the day before.
Peter confessed that he ate all the cake the day before.

8) “I feel very well now.” (he/explain)
He explained that he felt very well by then.

All the others are fine. What I've written in italics are additional ways to write the same ideas.

Yes, the sentences are correct. Here's a breakdown of each sentence and the explanations:

1) “I met Mary last Monday.” (she/say)
- The reported speech form of this sentence would be: "She said that she had met Mary the previous Monday." To change the tense, we use "had met" to indicate the past perfect tense.

2) “I’m sorry, I broke the vase.”
He apologized for breaking the vase.
- This sentence is already in reported speech form, so it doesn't need any modifications. The person simply apologized for what they did.

3) “ You should really read this book, Steve! (Sally/recommend)
Sally recommended I should really read that book.
- In reported speech form, we can use "recommended" to indicate that someone advised or suggested something.

4) “ Be careful, because the roads are slippery.” (The policeman/warn/us)
The policeman warned us to be careful because the roads were slippery.
- The reported speech form of this sentence would be: "The policeman warned us to be careful because the roads were slippery." We maintain the tense of the verb and use "were" to indicate the past tense.

5) “I’ll help you.” (my mother/promise)
My mother promised that she would help me/to help me.
- This sentence can be reported as: "My mother promised that she would help me" or "My mother promised to help me." Both variations are correct.

6) “We went on a school trip today!” (Peter/tell/his mother)
Peter told his mother that he had gone on a school trip that day.
- The reported speech form of this sentence would be: "Peter told his mother that he had gone on a school trip that day." We use "had gone" to indicate the past perfect tense.

7) “ I ate all the cake yesterday.” (Peter/confess to)
Peter confessed to eating all the cake the day before.
- The reported speech form of this sentence would be: "Peter confessed to eating all the cake the day before." We maintain the tense of the verb.

8) “I feel very well now.” (he/explain)
He explained that he felt very well then.
- The reported speech form of this sentence would be: "He explained that he felt very well then." We maintain the tense of the verb.

9) “Will your mother be at home tomorrow?” (Mary/ask/me)
Mary asked me if my mother would be at home the next day.
- The reported speech form of this sentence would be: "Mary asked me if my mother would be at home the next day." We change the tense of "will" to "would" to indicate future in the past.