I want to help answer popular questions that haven't been answered yet (since answers to these questions would be much-demanded by Google searchers and Stackoverflow users). Is there any way to find unanswered questions on Stack Overflow (in order of descending popularity, i. e., view count)?
If by popularity you mean votes, you can find a list of unanswered questions sorted by votes here.
If you want to include views, you will have to use
See the search tips listed here.
Regarding your comment about filtering out closed questions, you can add