1. Yes, I meant the first player and the second player.
2. Indeed, each player will meet all the other participants in the first
phase only if there are exactly seven participants. I didn't think of a
better term than round-robin, but there should be one.
3. The worst mistake. I copied and pasted Fergus' page for GCT#2 and
applied it to a different situation. (GCT#1 and GCT#2 are true
round-robins.) I think I'll follow your link.