This additional cost is informally known as the "commander tax." If you're casting your commander for an alternative cost, such as "without paying its mana cost" or a bestow cost, the commander tax applies in addition to that alternative cost
Funnily enough, I had a quick look at the Cloudpost deck that made the Top 8 of the very first Modern Pro Tour in Philadelphia back in 2011, and the deck contained four cards that are now banned Cloudpost, Eye of Ugin, Green Suns Zenith and Punishing Fire
Everyone knows this, and everyone knows that everyone else is also eager to buy those $1.50 $2.00 Den Protectors before they double or triple in price
Yes, flip cards keep counters
Credit where credit is due, though, to anyone who can win consistently with an Epic Struggle deck
And when Artificial Evolution resolves, you change every instance of Mutant on Genghis Frog to Frog. So from now on, Genghis Frog effectively reads: Whenever Genghis Frog or another Frog you control enters, create a Mutagen token. Now we let the original Genghis Frog trigger resolve