Tank doesn't have to kill the nail, the dps should be enough for it. If the tank moves to the nail(s) Ifrit will roast them and the rest of the party. If you are struggling to down the nail in time, your dps are doing something wrong, either skill or gear wise. As much as I don't like it, the game has constant roadblocks when it comes to gear.

Also, you CAN watch all cutscenes in your inn, they are not all under the same category though. Just change to duty and you should be able to find it.