Most countries have laws about what is ethically appropriate. In Canada, you cannot ask most personal lifestyle questions, like marital status, faith, ethnicity, parental status, etc., The issue of law is dependent upon the country. Morally or ethically, interviews should be respectful and respect basic ethical principles.

In Sweden we have a pioneer scientist in this matter - Rurik Löfmark.

We used to work at the same department at Lund University and I Believe that the attached publication will be a good way for you to start.

Best regards - Pontus

There is a big confusion between compliance and ethics within the realm of business ethics. Most answers you got above are about compliance - not breaking any laws or soft laws (codes of conduct). The question about ethics of such an interaction would be much harder to answer though as this is one of the many situations within  business ethics where obligations toward the employer, your own interests and the obligations toward another human being within society cross and possibly can come into conflict with each other. Sorry I don't have a paper on this at hand, but I thought you might find avoiding this popular conflation useful.

Laws about what is appropriate vary greatly between different jurisdictions. In Canada, as noted above, there are a number of proscribed areas that in other cultures are expected questions. Ethics is not the same as law or custom.

In general, the ethics of interviewing would seek to ensure that there is no bias that would exclude a candidate on the basis of non-relevant criteria (or non-legal criteria in some contexts). For instance, if the job does not require communication skills as a bona fide requirement, such as a job in customer relations, the interview process should not create a situation in which someone who is working in their second or third language would be disadvantaged.

Other ethical considerations would be those around encouraging diversity. A selection process that unfairly privileged male applicants over female applicants, for instance, would be less ethical because it undercuts the principle of equality (plus, it inappropriately handicaps a significant population).

Basic ethics then would include processes that would not unfairly disadvantage particular populations.

Another level of ethical consideration in an HR interview would be what we might consider "common courtesy" (recognizing that this is culturally determined). This might mean that it would be considered unethical to ask about someone's sexual history as part of a job interview, political beliefs, religious beliefs, or their attitude towards particular sports teams.

The principle of "bona fide" requirements is the important guideline: which aspects of a person's personal or professional life can in good faith be considered applicable to their job performance.

In one company I got a chance to be interviewed, its manual of operations states that panelists can only ask questions approved by the company.  At any point the interviewee feels the questions are invasive or out of scope, she may opt out of interview or call the attention of panelists about the matter.  In such case, panelists have to extricate that segment of interview from the report without prejudice to the interviewee.