The ability to bounce is pretty strong, yeah, I'll consider increasing its randomization cost so it isn't as easy to get.
The logic for attacking and exhausting (tapping out) is the following. "If you attacked or blocked, your Minion gets exhausted at the end of the turn." So you can choose to either attack and use your exhaust ability by the end of the turn. You can choose not to attack so you can block and/or use that exhaust in your opponent's turn, or you can just exhaust during your turn without attacking.
Regarding the dungeon being open before finishing the "quest", I thought about doing exactly as you said, but I figured I'd give the user the option to just go. But thinking about it maybe not the best idea this early in development.
I'll think about the life totals. I'm also going to implement an attack power limiter so any of your opponent's low-cost creatures have more attacks than your starting hp so you don't die turn 1 or 2 .
Also, the fact that you downloaded and played is very troubling, I thought I'd dealt with the targeting bug. I guess there's still something wrong there. Thanks again for all the feedback and info, very helpful!