I dont believe there is any endpoint that will retrieve a count, but you could retrieve the actual content for that user and count it yourself.
To retrieve the questions for a user you can use the Content Service: https://developers.jivesoftware.com/api/v3/cloud/rest/ContentService.html#getContents(List<String>, String, int, int, String, boolean, boolean) and utilize the author and type filters.
I'm not sure if there is a filter for just questions versus all discussions. You may need to exclude the non-questions after getting the response.
You could also use Jive's v3 Search API (https://developers.jivesoftware.com/api/v3/cloud/rest/SearchService.html#searchContents(List<String>, List<String>, boolean, boolean, boolean, boolean, String, int, int, String, boolean, String)) and use the subType param as question to get only questions. However, the search API will always expect a mandatory search query and the results are paginated. So, to get the count, you will have to manually call each of the "Next" endpoints till you reach the end and calculate the total count.
It would be really helpful if Jive had provided the total number of results for the search or content v3 API. I have added an Idea requesting for this feature -Jive's core APIs should return the total number of results