Difference between 留神，留意，留心？
You should understand the three characters in the words firstly.
心：Mind
意：Sense
神: Focus

So add 留(keep) before them, becomes:


留心：Keep in mind --> remember
留意：Keep in sensitive --> ?
留神：Keep on focus  --> look out / be careful


My translation may not accurate in English, if someone have better translation, please comment below.

In your example, 


sentence 1 talking about reading/studying, so 留心 should be the only correct word. 
Sentence 2, here 留心 is separated, it's a derivative usage in my opinion. It means "keep defensive (because I remember he did something bad.)". 
Sentence 3, I don't understand the meaning... and I don't want to guess (although I could) since it's a tutorial/exam, it should be clear.