There is a call that return the number of total questions by tag https://api.stackexchange.com/2.2/tags/java/info?order=desc&sort=popular&site=stackoverflow
But how would you get the number of unanswered questions by tag?
For unanswered questions, use the /questions/unanswered
route:
api.stackexchange.com/2.2/questions/unanswered?tagged=java&site=stackoverflow&filter=total
For questions with no answers, use the /questions/no-answers
route:
api.stackexchange.com/2.2/questions/no-answers?tagged=java&site=stackoverflow&filter=total