The answer is your first option<u>: thank the interviewer for his or her time</u>
Explanation:
Saying thank you for the time at the end of the interview, gives the interviewer a good impresion as well, as it is a way of being polite and showing empathy for the other's valued time. On the other hand, asking how the interview is going is sort of rude or innapropriate as you need to go along with the flow of it, not ask! Finally, gathering references and a resume should be done before the interview, when the interviewer contacts you for an interview, it is because he has already seen your resume/CV and has liked your profile for the position, also, this is gathered by the interviewer not the interviewee, on difference with the other two options.
