"What do you think the best method to show time left for active background (wolf, rolling stone)?"
Probably floating text that moves with camera. So a player wouldn't need to have his/her eyes constantly glued to place where wolf/stone/etc should be. Beside, speical audio effect to indicate that wolf/stone/etc became avaiable would be helpfull too.
"Also there is a chance that player can cheat the game."
Of course. By the way, it's why I susggested number of wins, instead of win/lose ratio (otherwise a player would be able to cheat by allowing enemies to kill him). But the same logic is applied to any code. A player with some hacker skills can find a bug and use it to cheat the game. But would you give up? "I can't write perfect code, thus I should just give up". I don't think so, most likely you would just change your code. You can use the same approach in proposed price mechanism. If you will discover (or a player will discover and inform you) way to cheat it, then you can always just change how the price mechanism works. Or even return to static prices, if you decide that you can't fix it.
Another advantage of dynamic prices: As a developer you can include new bonus (or remove/change old one) without need to carefully recalculate static prices.
P.S. Among with cheating, there is another possible problem with dynamic prices: Price adjustment takes time. Considering relatively small amount of missions (18 missions total. 19 if we count bonus mission with the giant green ogre.) prices must adjust quickly enough (probably giving ability to replay guild missions and make them able to influence the prices will ease this problem a little.).