I can answer the first question: a map that's been a contestant for map of the week once can never be eligible again; unless it was the runner up, in which case it's an automatic contestant for the following week.
I can also answer the last question: you don't get any kind of notification unless some player goes to the trouble of sending you a message about it.
Statistics would be interesting, but I don't have any at hand.
Edit: Oh, also, if you go to the list for all maps of the week, here: https://www.warzone.com/MapOfTheWeek/
you can search for names and see how often they appear. NinjaNic has won 7 times (as have I), Colion 14, and Lionheart 25.
Edited 1/30/2021 01:31:30