All suggestions are purely for style. No red this time.
*Jim and Tim were at the library. They were each reading a storybook. Jim was engrossed in reading the storybook. Tim found the storybook boring. He was so disappointed that, on the spur of the moment, he ripped one of the pages of the book.
*You have written four very short sentences, in which the word "storybook" is repeated three times. Why not combine four into two? Jim and Tim were at the library, each reading a storybook. Jim was engrossed, but Tim was bored. Here also is your opportunity to use the present participle in an adjectival phrase.
A girl saw what he did and went to inform the librarian, who went to where Tim was sitting and confronted him. He was lost for words. “Come to the counter with me,” she demanded. At the counter, she scolded him and asked him for his home telephone number *as she wanted to inform his parents about his misdeed. He refused to comply at first. The librarian then threatened to report him to the police. On hearing that, he was frightened and told her the telephone number. She spoke to his mother, who apologised **to her for what her son had done. She promised to pay for the book and told her that she would punish her son when he came home. Tim’s mother also scolded him on the phone and told him to tell the librarian that he was sorry for his stupid act. Tim complied by telling the librarian that he regretted his action.
*Here you whould either put a comma before the "as", or strike out "as" and replace it with a colon: ...number: she wanted... . Without the comma, "as" might on first glance mean not "because", but "while, during which time". The colon serves the identical purpose: it introduces and explanation for what is written just before it.
**Since parents usually have to apologise for their children to authority figures, to her does not add to the meaning; you may want to omit it.
Since that incident, Tim has never gone to that library. He *is ashamed to be seen by the librarian again.
*This is not an error! Good use of "is" as opposed to "has been".