The FA site says this: "A shortlist of three nominees is selected by The FA on the Monday morning after after each Round. Fans can then vote on-line for the player they feel should win the prestigious award by visiting www.thefa.com. We announce the winner on the Friday afternoon" Although that explanation was from a few years back and it may have changed since - I certainly couldn't find the voting page.
Not really They've played a game, so all teams judged on 1 game, would be unfair to allow some teams 2 games to be judged on.