Is it fine to ask this kind of question to the corresponding author of a paper? First some context: I'm a Ph.D. student in Physics. I have been discussing with my supervisor the objectives for the Ph.D. project and we have been looking at some papers from the field.

In that case, recently I've come across a quite interesting paper, one of the authors being a very renowned researcher in the field. The paper raised a conjecture and pointed out that one what was necessary to follow that line of investigation in order to prove or disprove the conjecture. I got quite interested in pursuing this objective and my supervisor considered it to be a good idea for the project.

It so happens that a few days after, I have found a paper by another author, which is also a quite renowned researcher, briefly disputing the claims made in the first paper.

Given my current knowledge, I would consider that the authors of the first paper are correct, but of course I might be wrong. 

Now, the first paper is three years old and the authors didn't revisit the issue in another publication.

I considered the possibility of contacting the corresponding author and asking about the comments made in that response paper. In particular I would like to ask if they changed their view on the problem after all or if I'm correct in my conclusions and they still believe in their first proposition.

Also I considered asking if he still views that as a line of investigation worth pursuing.

Are that kind of questions considered ok or are they viewed as unethical? My worries are: (1) if I can indeed ask for his views on that brief response and if it made then revisit their positions and (2) if it is ok to ask if he considers a good idea to pursue this objective.
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.