Huh, confusing..
Each round lasts 1 week and during this time the players must finish the chess game. A chess game can consist of any number of duels, it depends on the players. Duels are best of 3 - the first to win two wins the duel, and the other piece is removed. Decks can be swapped anytime, but it will take effect only in the next round, so only in the next chess game, against the next opponent.
So, in summary:
Round: lasts 1 week, this consists of chess games (matches/matchups)
Chess game: the chess game itself, pieces moving and dueling, etc.
Duels: best of 3 games
Does this clarify it?
I'm not sure if best of 1 is a good idea. Did you see the chaos it caused in War? We'd like to avoid that.