Do the skin models come with the relevant character cards? I want to be able to play mirror matches or at least have the possibility for the same character to appear on both teams for the base minis and don't really want to have to buy another copy of the game to get the cards...
No, just the skin and the character stat card, but no extra tactics. You can still play mirror matches though, sharing the core tactics cards.
I agree that theoretically you can share the character specific Tactics cards because there are four and each player may choose two. However that practice does mean that if you have two, then you know that your opponent has the other two rather than the choice being secret. I suppose that you can shuffle the four and deal each two and then neither player would know which cards are in their own deck. That might make for interesting and surprising play!
You can print the cards out yourself, https://aristeiathegame.com/downloads Its a bit of work with the cut-out but after sleeving them there is nor really noticeable difference. Especially if you use 120gramm paper for printing