Gravial Archetype [Written]

[Archelaus]

Catalyst of the Gravial
Level 4
DARK/Fiend/Effect
During either player's Main Phase (Quick Effect): You can reveal 1 "Gravial" monster from your hand; send 1 monster with the same name from your Deck to the GY. When this card is sent from the field to the GY; send 1 "Catalyst of the Gravial" from your Deck to the GY. During either player's turn (Quick Effect): Banish this card and another card with the same name from your GY; Special Summon  1 Level 4 or lower "Gravial" monster from your hand. You can only use each effect of "Catalyst of the Gravial" once per turn.
ATK/ 1600 DEF/ 1600

Reckoned of the Gravial
Level 4
DARK/Fiend/Effect
Once per turn, during your Main Phase: you can banish 1 Level 4 or lower "Gravial" monster from your GY; Special Summon 1 monster with the same name from your Deck. When this card is sent from the field to the GY: send 1 "Reckoned of the Gravial" from your Deck to the GY. Banish this card and another card with the same name from your GY (Quick Effect): Draw 1 card. You can only use each effect of "Reckoned of the Gravial" once per turn.
ATK/ 1700 DEF/ 1200

Impulse of the Gravial
Level 4
DARK/Fiend/Effect
When this card is Summoned: Send 1 "Gravial" monster from your Deck to the GY. During either player's turn (Quick Effect): Banish this card and another card with the same name from your GY; Select 1 face-up "Gravial" monster you control and send all monsters with the same name from your Deck to the GY; When this card is sent from the field to the GY: send 1 "Impulse of the Gravial" from your Deck to the GY. You can only use each effect of "Impulse of the Gravial" once per turn.
ATK/ 1200 DEF/ 2000

Inhibitor of the Gravial
Level 4
DARK/Fiend/Effect
During either players' turn, when a Spell or Trap Card is activated (Quick Effect): you can send this card from your hand to the GY and banish 2 "Gravial" monsters with the same name from your GY, except "Inhibitor of the Gravial"; negate that card's activation and effect, and destroy it. When this card is sent from the field to the GY: send 1 "Inhibitor of the Gravial" from your Deck to the GY. You can only use each effect of "Inhibitor of the Gravial" once per turn.
ATK/ 1600 DEF/ 1000

Initiator of the Gravial
Level 4
DARK/Fiend/Effect
Banish this card from your GY: Special Summon 1 "Initiator of the Gravial" from your Deck. When this card is sent from the field to the GY: send 1 "Initiator of the Gravial" from your Deck to the GY. You can only use each effect of "Initiator of the Gravial" once per turn.
ATK/ 500 DEF/ 200

Caller of the Gravial
Level 4
DARK/Fiend/Effect
When this card is Summoned: You can banish 1 "Caller of the Gravial from your GY; Add 1 "Gravial" monster from your Deck to your hand and send 1 monster with the same name from your Deck to the GY. When this card is sent from the field to the GY: send 1 "Caller of the Gravial" from your Deck to the GY. You can only use each effect of "Caller of the Gravial" once per turn.
ATK/ 1800 DEF/ 800

Rectant of the Gravial
Level 6
DARK/Fiend/Effect
During either player's turn (Quick Effect): You can banish 1 face-up "Gravial" monster you control and send 1 monster with the same name from your Deck to your GY; Special Summon this card (from your hand). Once per turn, during your Main Phase: you can banish 1 "Gravial" monster from your GY and send 1 monster with the same name from your Deck to the GY; Special Summon 1 "Gravial" monster from your Deck, except "Rectant of the Gravial". When this card is sent from the field to the GY: send 1 "Rectant of the Gravials" from your Deck to the GY. You can only use each effect of "Rectant of the Gravial" once per turn.
ATK/ 2000 DEF/ 2000

Denuos, the Cataclysmic Gravial
Rank 4
DARK/Fiend/Xyz
2 Level 4 monsters
While this monster has an Xyz Material attached to it: it gains 300 ATK and DEF for each monster in your GY. During either player's turn, when a monster is Summoned (Quick Effect): you can detach 1 Xyz Material from this card and banish 2 monsters from your GY; negate the Summon of that monster and banish it. When this card is sent from the field to the GY: send 1 "Denuos, the Cataclysmic Gravial" from your Extra Deck to the GY. You can only use each effect of "Denuos, the Cataclysmic Gravial" once per turn.
ATK/ 1000 DEF/ 1000

Mythirr, the Dawn Gravial
Rank 4
DARK/Fiend/Xyz
3 Level 4 monsters
While this monster has an Xyz Material attached to it: Dark Fiend-Type monsters you control cannot be destroyed by card effects. Once per turn: You can detach 1 Xyz Material from this card; Special Summon 1 Level 4 monster from your GY and send 1 monster with the same name from your Deck to the GY. When this card is sent from the field to the GY: send 1 "Mythirr, the Dawn Gravial" from your Extra Deck to the GY.
ATK/ 2500 DEF/ 2000

Hecotep, the Bulwark Gravial
Rank 6
DARK/Fiend/Xyz
2 Level 6 monsters
While this card has Xyz Materials on it: other monsters you control cannot be destroyed by battle or by card effects. Once per turn, during either player's End Phase (Quick Effect): you can detach 1 Xyz Material from this card; add 1 "Gravial" monster from your Deck to your hand and send 1 monster with the same name from your Deck to the GY. When this card is sent from the field to the GY: send 1 "Hecotep, the Bulwark Gravial" from your Extra Deck to your GY
ATK/ 3000 DEF/ 1800

Gravial Sanctuary
Field Spell Card
You can banish 2 "Gravial" monsters in your GY; Draw 1 card. "Gravial" monsters gain 300 ATK for each monster with the same name in your GY. If this card is destroyed by your opponent's card: Special Summon 1 Level 4 "Gravial" monster from your Deck. When this card is sent from the field to the GY: send 1 "Gravial Sanctuary" from your Deck to the GY

Tempest of the Gravial
Normal Spell Card
Return 2 "Gravial" monsters with the same name from your GY to the Deck: draw 1 card. When this card is sent to the GY: send 1 "Tempest of the Gravial" from your Deck to the GY.

Gravial Funeral
Normal Spell Card
Send 1 "Gravial" monster from your Deck to the GY. When this card is sent to the GY: send 1 "Gravial Funeral" from your Deck to the GY.

Burial Stance
Quick-Play Spell Card
Banish 1 "Gravial" monster in your GY: send up to 2 monsters with the same name as the banished monster from your Deck to the GY and add 1 Level 4 "Gravial" monster from your Deck to your hand. When this card is sent to the GY: send 1 "Burial Stance" from your Deck to the GY.

Ordinance of the Gravial
Counter Trap Card
When a monster would be Summoned, OR when a Spell Card, Trap Card or Effect Monster's effect is activated that includes an effect that Special Summons a monster(s): banish 2 "Gravials" monsters from your GY; negate the Summon or activation and destroy that card. When this card is sent from the field to the GY: send 1 "Ordinance of the Gravial" from your Deck to the GY.

[Darj]

It's nice to see you have a decent grasp on card text formatting and PSCT. And yet... you have mistakes all across the cards, and even some texts you write right in a card, but you write them wrong in another one. I find that a bit odd. Your most glaring mistake is writing "during either player's turn". That sentence is outdated and now it's integrated in the "(Quick Effect)" clause. That means you no longer have to write the "during either player's turn" line. Also in other cases, you out the "(Quick Effect)" clause after the cost, when it goes before costs. In other cases you give an "once per turn" to an effect, but then end the card with a "You can only use each effect of X once per turn" making the first OPT clause redundant.
Fixing Catalyst, it would look like this:
During the Main Phase (Quick Effect): You can reveal 1 "Gravial" monster from your hand; send 1 monster with the same name from your Deck to the GY. When this card is sent from the field to the GY; send 1 "Catalyst of the Gravial" from your Deck to the GY. (Quick Effect): You can banish this card and another card with the same name from your GY; Special Summon  1 Level 4 or lower "Gravial" monster from your hand. You can only use each effect of "Catalyst of the Gravial" once per turn.

Anyway, these look solid enough. They got staple effect like searching, Special Summoning, a couple of negations. I'm curious about their gimmick though: sending copies of themselves to the GY. Most cards do it, even the Spell/Traps, and while copies are needed to activate some of their effects, I have yet to find how the Spell/Traps and Xyzs benefit from sending copies of themselves to the GY. I was wondering if a Field Spell or otherwise key card of the archetype would let you retrieve cards from the GY if there is another copy of them in the GY, but I don't see such effect. All I see is them grabbing from the Deck, and sending a copy from Deck to the GY, restricting the number of times you can use the effect to 1 unless you run Deck-restacking effects.