Am I right - if I have not Google API key then Persons and Online Profiles will not work in module Locations Map?
Is any way to use Locations Map for Persons without GoogleMaps API key?
The Locations Map just takes locations (latitude/longitude paris) and displays it on a map. It doesn't making any geocoding neither it adds locations on its own. So, yes, if you don't have a working Location field on your profiles then UNA will not be able to geocode those profiles, so no any locations will be determined and thus the Locations Map will not be showing anything since there will be nothing to show.
And no in the current UNA version there is no way to change the way geocoding works, Google's geocoding is hardcoded there. According to this discussion this may change in UNA 11.