At the moment, your title asks "Is it ethical/professional to give feedback to an interviewee during an interview?", while the body of the question mentions your interviewees are interested to hear immediate feedback right after the interview.

This may actually be an important distinction. If you are asking questions and perhaps doing tasks during an interview, discussion of what might be a good (or better) answer/approach is often a natural part of the interview process, and will tend to be quite matter-of-fact in nature, as well as giving the candidate a second chance to challenge your impression (which may itself be illuminating). The candidate will probably get some idea of how they are doing as the interview progresses.

Feedback after an interview is more likely to be seen as an indication of how likely the candidate is to progress to the next stage, which may be unfair to everyone if that's not your decision, and perhaps runs more risk of seeming subjective or unfair, especially if the feedback is negative. Also, you are usually going to be in the position of weighing the candidate against others you have seen - which may be better done in a situation where you haven't just spent a couple of hours with the candidate.

On a related point, you should probably leave most candidates feeling that they could have done a little better - if not, you probably haven't pushed them quite hard enough!

At the moment, your title asks "Is it ethical/professional to give feedback to an interviewee during an interview?", while the body of the question mentions your interviewees are interested to hear immediate feedback right after the interview.

This may actually be an important distinction. If you are asking questions and perhaps doing tasks during an interview, discussion of what might be a good (or better) answer/approach is often a natural part of the interview process, and will tend to be quite matter-of-fact in nature, as well as giving the candidate a second chance to challenge your impression (which may itself be illuminating). The candidate will probably get some idea of how they are doing as the interview progresses.

Feedback after an interview is more likely to be seen as an indication of how likely the candidate is to progress to the next stage, which may be unfair to everyone if that's not your decision, and perhaps runs more risk of seeming subjective or unfair, especially if the feedback is negative. Also, you are usually going to be in the position of weighing the candidate against others you have seen - which may be better done in a situation where you haven't just spent a couple of hours with the candidate.

On a related point, you should probably leave most candidates feeling you've touched on areas where they still have some learning to do - if not, you probably won't have challenged them enough to give them the chance to show what they are capable of.