Let's start with Infernity Reflector:
Activate only by discarding all the cards in your hand when an "Infernity" monster you control is destroyed by battle and sent to the Graveyard. Select and Special Summon that monster from your Graveyard, and inflict 1000 damage to your opponent.
This Normal Trap Card is activated at the End of the Damage Step. Discarding your hand is a cost, and it targets the destroyed Infernity monster. The damage and the Summon are simultaneous. As a side note, you need at least 1 Card in your Hand to activate Reflector.
Next, we have Infernity Break:
Activate only if you have no cards in your hand. Select 1 "Infernity" card in your Graveyard and remove it from play. Select 1 Card your opponent controls and destroy it.
Break targets two Cards, one in your Graveyard, and one on the opponent's side of the Field. Break will resolve properly even if you have Cards in your Hand during its resolution. The destruction and the removal are considered to be simultaneous. If your Card is no longer in the Graveyard, then you do not destroy the other target, but if the opponent's Card is no longer on the Field, you still Remove your Card from Play. Note that Infernity Break can use any Card with "Infernity" in its name, so you can use Cards like Infernity Launcher or even another copy of Infernity Break.
Moving on, we have Infernity Inferno:
Discard up to 2 cards and send the same number of "Infernity" cards from your Deck to the Graveyard.
Inferno has no cost. You actually discard the Cards as part of its effect, so it works with the effects of Dark World monsters. Once you activate Inferno, you must discard at least one Card. After you discard, you will send the same amount of "Infernity" Cards from your Deck to the Graveyard. Once again, notice that you are not restricted to Infernity monsters.
The following Card lacks the Infernity name, much like ZERO MAX, but it still blends with the theme. Let's take a look at Phantom Hand:
Once per turn, if you control a face-up "Infernity" monster(s), you can remove from play all cards in your hand (face-down) until your next Standby Phase.
In order to resolve Phantom Hand's effect properly, you must control an Infernity monster upon its resolution. Once you do, the Cards that were in your Hand are not related to Phantom Hand anymore, so even if PH is no longer face-up, you will still recover the Cards during your Standby Phase. Of course, if Phantom Hand is destroyed in a chain to its effect that Removes your Hand from Play, it will resolve without effect, as it is a Continuous Trap Card. Note that Phantom Hand has a Spell Speed 2 effect, so not only you can activate it during your opponent's turn, but also, you are able to chain it to most effects. For example, if your opponent activates Torrential Tribute when you Summon Infernity Guardian, you can chain Phantom Hand's effect to protect Guardian.
The last Trap Card and Infernity support in the set is the TCG exclusive Infernity Barrier:
Activate only when your opponent activates a Spell Card, Trap Card, or Effect Monster's effect, if you control a face-up Attack Position "Infernity" monster and have no cards in your hand. Negate the activation and destroy that card.
Barrier is an extremely simple Counter Trap Card. If you meet its activation requirements, it negates almost anything. It's easier to list what Barrier cannot negate, which are the effects of already active S/T Cards, and effects that do not use the chain like Jinzo. Some people simply read it as a copy of Solemn Judgment, which leads to believe it also negates Summons, but this is not true for Summons that aren't performed through an effect that uses the chain. For example, Barrier can negate the effect of Gorz, but it cannot negate the Special Summon of Cyber Dragon.
And that's all for Infernities so far. Stay tuned for more TSHD goodness. If you have any questions, feel free to drop me an e-mail at ness00[at]gmail[dot]com.