Hi Lisa! Are these questions in groups or spaces or both? For spaces, there is a feature in the admin console that allows you to enable email alerts for open questions older than x hours.
Otherwise, you will have to write some code (or have our PS or a partner do it).
Use the /contents endpoint to get all content of type discussion in a specific place and sort the list by latest activity descending.
Then iterate over the returned set and look for the Boolean "question" (https://developers.jivesoftware.com/api/v3/cloud/rest/DiscussionEntity.html) to determine if the object is a question. Then check to see if the replyCount is 0. If these are all true, add the question to a list.
So there isn't a single call that can get you this information that I can see.