Hello Debbie,
Questions are not stored into quiz. Absolutely all questions are in the question bank and all questions have a category.
Most probably if your teacher "did not use categories when creating quizzes" these questions are in the default category for that quiz in the question bank.
You can either export these questions from this category and import them into the one where you want to use them (I suggest using MoodleXML format), or read the documentation about sharing questions between courses