The nightmare damage is a consequence of having your hand filled, therefore the damage is not reflected by reflective shield. Also, we really need more info on what was this so called "thing" they targetted that was "indestructible".
If the game allows you to connect to someone and you automatically lose, not a desynch, the problem isn't the PvP servers. It's you. Well, rather, your internet connection. I know this from sad experience.
There are already "Marks" that show if it is rare. On the left of the name, there should be something similar to "Shark Fins" (or so I've heard.) The more the merrier. The codes are already a way to change quickly. Battle log may take too much stress upon our already frail server.
There's a whole section for card ideas in the forum. This is a side project for zanz, as I have said a billion times. We should be glad it's even updated at all. Further on, adding cards requires coding, fixing bugs, AND fixing the card (You can't just throw in a card without making it decent, not OP or UP, right?)
I don't know how many times this has been said. The game HAS an AUTO mulligan feature. It happens only once. If you get that problem so often, chances are the problem is your deck.