Since the clues are in descending order of difficulty, let's do this one backwards:
My whole's population growth did recently flatten
Must be China. Let's see if we can't cram the rest of the clues in..
My infix a greeting, modernly its excitement subjective
My prefix a strange domain, unless you know Latin
ch is the top level domain for Switzerland, from "the Confederation of Helvetia", or more historically accurately, the Latin version thereof
My suffix is western, from a "western" perspective
NA, for North America, is the western part of the occident, or "the west" as it's also called.