Is this game free? Yes, play without ever spending a penny.
Can I trade my cards with other players? Yes.
Is there a limit on how many cards I can get per day: No, play as long as you want, when you want, and get cards from how long you play.
Are all cards playable forever or are there rotating sets: All cards are playable forever.
What's the best way to meet other Domain players and get multiplayer games: On the discord linked here: Discord.