Is it fine to ask this kind of question to the corresponding author of a paper?
Your advisor will give the best advice, of course, especially if he knows any of the people involved. But in general there is no ethical reason you can't ask such questions of an author. 

But I might phrase it differently. I'd probably ask if there is any current work on the topic that will shed more light on the questions. And your suggestion of asking if they think it is a good line to pursue is good also, I think. Express your interest in the topic and that you are considering it as a research topic. 

But I wouldn't couch the question in terms of responding directly to a (partial) rebuttal if that's how you judge the new work. It doesn't sound like that is the case, though, so just asking about what they can tell you about current thinking and research is fine. 

And, if they are working on the topic it might save you from the problem of going along on a parallel track and getting scooped by more experienced researchers.