Yes, they are taught to give a signal but like the infield fly signal, it doesn't always happen.
Yes, it does appear from the replay that the run was counted in error.
Yes, it did impact the final score although I would not go so far as to say it cost Washington the game (but then I still don't think Don Dinkingers call cost the Cardinals game 6 in '85 either).
Wrong, I have seen even a "decent HS crew" kick this call as well. Never one of my games though
.