I believe that the short answer is yes. However, trying to describe the variety of methods will take too long.
The best thing to do is to set up a sandbox Moodle, and experiment.
A set of questions can be shared among many quizzes. If you want similar, but not exact questions, yes, you can duplicate the beginning set and put them into their own separate category. And there are ways to share some questions, yet keep some unique. Experimentation will go a long way to learning Moodle's powerful quiz system.