Between which months does UNM conduct interviews and when is the latest that I can interview to get into the following incoming class?

Interviews start as early as September for the early admit group. They are conducted as late as mid February.
Theoretically anyone can interview as late as February but the class is starting to fill by early February with the rolling admissions and the class is really taking shape by that time.

Admissions usually suggests interviewing in mid Nov to early December. Then try to interview just after the holiday break and thru January to get the best out of the interview.