Could you check the following sentences on indirect speech, too? Thank you.

By the way, how do you pronounce "Keruac", the surname of the famous American writer?

1)He invited me to go for a walk.
2)One of the guests apologized for breaking the vase.
3)He suggested I should book for the play in advance.
4)He reminded me to turn .. (when I had finished)
5)He admitted eating all the cake (the previous day).
6)He denied breaking the vase.
7)He refused to answer any questions.
8)She agreed/promised to drive me to the airport.

http://www.forvo.com/word/jack_kerouac/

Click on the sideways triangles (both of them) to hear the name pronounced.

All the sentences look good except 3, and I'm wondering how you will complete 4.

In 3, do you mean "buy a ticket" for the play... ?

To check the sentences on indirect speech, we need to change the verb tense and pronouns to reflect what someone said. Here are the revised sentences:

1) He said, "I invite you to go for a walk."
2) One of the guests said, "I apologize for breaking the vase."
3) He suggested, "You should book for the play in advance."
4) He reminded me, "Turn when you have finished."
5) He admitted, "I ate all the cake the previous day."
6) He denied, "I broke the vase."
7) He refused, "I won't answer any questions."
8) She agreed/promised, "I will drive you to the airport."

Now, to pronounce "Keruac," the surname of the famous American writer, Jack Kerouac, you can break it down into syllables like this:
Ke-ru-ac

The "Ke" sounds like the letter "K," the "ru" sounds like "rew," and the "ac" sounds like "ack." So, it would be pronounced as "Ker-rew-ack."

I hope this helps! Let me know if you have any further questions.