1. Wrong: Ilya looked at book for the several hours before she had quiz.
Better: Ilya looked at the book for several house before she had a quiz.
Explanation: She's looking at one specific book, but taking one of many quizzes. Severalalready gives the number, so the is unnecessary preceding it.
2. Wrong: Li Jing gave bag he found to police officer.
Better: Li Jing gave the bag he found to a police officer.
Also better: Li Jing gave the bag he found to the police officer.
Explanation: Li Jing presumably found just one bag, so that noun needs to be preceded by the. The first sentence correction assumes that Li Jing saw a variety of officers, while the second sentence assumes that Li Jing saw only one officer to whom to give the bag.
3. Wrong: Marquis won spelling competition for eighth year in a row.
Better: Marquis won the spelling competition for the eighth year in a row.
Explanation: The speaker is talking about a specific competition, not one of many Marquis competes in. The is needed before the ordinal number eighth.