A few hints from an old player: You can ask as many other player to ally as you like. The ships are stackable, they are much easier to manage if you stack them. For clarity, place defending allies next to the planet rather than on it, so they don't get mixed up with other colonies. You need to be a little more orderly with alliance phase. It can cause issues if people choose a side before both offense and defense have made invitations. It is not much of a problem with 4 players but messy with more. It's good to see you all managing your way through the game, mistakes and all. Maybe someone should have played as Greenhorn.
Adam should've got 4 cards as compensation when he played the negotiate on his first defense, because 4 of his ships were sent to the warp (the place ships go to die), before being healed.
What a strange ruleset to choose races. My group has always shuffled the entire flare card deck, drawn 2x the amount of players and picked from the two random races we got.
By the way, the 42nd Anniversary edition rules are badly edited, unclear and mistake ridden. Take a look at the 2008 FFG rules set, the FFG errata and, most importantly, the Cosmodex on BGG.
Strange. I've heard other people say the 42nd Anniversary edition rules are better because of the use of examples, and the inclusion of the quick reference.