I left out these very last sentences on reported speech. Thank you very much!

1) “No, I didn’t break the vase.” (Mary/deny) Mary denied breaking ..
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 that Steve shoudl read that book. OR Sally recommended to Steve that he should read that book. (which one?)
6) “We went on a school trip today!” (Peter/tell/his mother)
Peter told his mother that they had gone ..... that day.
7) “ Yes, I ate all the cake yesterday.” (Peter/admit)Peter admitted eating all the cake the day before.
9) “Will your mother be at home tomorrow?” (Mary/ask/me10) “How about going to the cinema next Friday?” (Peter/suggest)
Peter suggested going to .... the following/next Friday.
“If I were you, I’d book for the play in advance.” (He/advise)He advise me to book for the play in advance.
12) “Oh, come on. Let’s go to the cinema tonight.” (He/insist) He insisted on going to the cinema that night.
13) “Keep off the grass!” (He/tell/me)He told me to keep off the grass.
She objected to travelling to London by train.

3. I'd write this: Sally recommended that Steve read that book. ("read" is subjunctive)

In 9, I don't understand the phrase "book for the play." Explain, please!

All the others are fine.

She objected to travelling to London by train.

To construct the reported speech for this sentence, we can follow these steps:

Step 1: Identify the reporting verb or phrase. In this case, the reporting phrase is "she objected to."

Step 2: Identify the reported speech. The reported speech is "travelling to London by train."

Step 3: Use the appropriate reporting verb or phrase. Since the original sentence already includes a reporting phrase, we can carry over the verb "objected" to the reported speech.

Putting it all together, the reported speech would be: She objected to my travelling to London by train.

Note that in reported speech, it is common to change personal pronouns, possessive pronouns, and verb tenses according to the context. Here, "she" and "my" were used to match the subject in the original sentence and the subject being reported.