Can I name my page/menu button something besides "question?" I'd prefer "questions" or "Your questions" or even "Q&A"

You mean something like this http://brainlubricator.com/questions/ yes you can go to your menu and add a link and write navigation label as Q&A or what ever you like and link as yoursitename.com/questions for this you need to change the permalink of your questions page using wordpress editor 🙂