Change these statements and questions to indirect speech and add them to the text.

You don't need to put the word "monster" in quotations for the story. She's just making a statement about seeing, hearing, or sensing some sort of a monster and so there's no need for quotations. As for the questions, they're all phrased properly. I highlighted one point in orange because it doesn't make sense with the punctuation. Remove the semicolon and it makes sense. If you use the semi colon, then you need to type the actual question you asked or her actual responses to your questions. The semicolon replaces the use of quotation marks here.

I asked her why she wasn't sleeping

I asked her: why aren't you sleeping?

I asked her: what is a monster?

I asked her, "what is a monster?"

The sentence marked in red doesn't make sense. I think you just got tripped up while typing it as it seems like the sentence in yellow is supposed to have taken place after it. As well, she didn't say if you had seen a monster, she asked. 

Do you know what a monster is? -no, have you seen it?

Make sure to check you messages for typos before posting them as there is a decent handful of them.

Hope that helps, feel free to respond with other questions pertaining to this post should you have more. :)

Change these statements and questions to indirect speech and add them to the text.

One time, when I was babysitting for some friends, their five-year-old daughter got out of bed and came into the living room. I asked her why she wasn´t sleeping. She climbed on to the sofa beside me and whispered that there was a (mister?) under her bed. I started to ask her where he had come from, then I realized that she had meant a monster. I asked her if she had seen the monster.  She said that she hadn't seen it, but she knew that it had big teeth. We eventually both fell asleep on the sofa and, luckily for us, the monster stayed in the bedroom.

The original text didn't make much sense.  Could you supply the original with the blank spaces?  

There are two aspects of reported speech that cause problems for students:

1)  Changing the person.

John:  I feel sick.

(direct reported speech) John said "I feel sick."

(indirect reported speech) John said that he felt sick.  ("I" becomes "he.")

2) Changing the verb tense.

"I feel sick."  ->  He said that he felt sick.

"I saw a monster." -> She said that she had seen a monster.

"I will go back to bed." -> She said that she would go back to bed.