If you are working on an individual research paper with the help of your advisor (e.g. M.Sc Thesis), what is the academic convention on asking for comments from other professors? For example, if your paper closely relates to a paper written by an author who is in another University, and hence might also be of interest to this author, would it be acceptable to mail him a copy and ask for his thoughts on the work, or could this be considered disrespectful towards ones own advisor?
It would be best to involve your advisor. I would advise against requesting comments from other professors without discussing it first.
It may be useful to approach your advisor and show them the work of the other professor to get their thoughts on the matter. They may agree, but they may also not wish to; mailing a copy without discussion would probably be interpreted as being disrespectful.
One thing to consider however is that the other professor may not offer comments on your paper. It may be that they struggle to find the time to peer review journal articles (which is pretty much a work obligation), so they may simply not have the time to offer comments on your work.
If you are hoping that mailing your paper may lead to the possibility of landing a PhD place, then you should consider sending your paper. However only do this following a discussion with your advisor, or after you have completed your thesis and received the award.