Yes, every time you start a battle you find out what the game rule, mana cap, and splinters available are. It's different every time.

Cockatrice is great for making your opponent waste attacks! If you're lucky and get a few misses in there, it lets the rest of your line up get tons of damage in.

No idea when it's going live, but it won't be too long from now. My guess is less than a week.