Eenie-Meenie-Miney-Tourach
Sorcery (U)
As long as Eenie-Meenie-Miney-Tourach is on the stack, players can't rearrange their hands.
Each opponent discards the card in his or her hand furthest to the left and the card in his or her hand furthest to the right

Invasive Vegetation |
Enchantment

Whenever a basic land touches a nonbasic land, that land becomes a copy of the basic land until ~ leaves the battlefield.

Matryoshka of the Damned -
Legendary Creature - Construct [M]
When ~ enters the battlefield you choose any number of creatures from your graveyard. Your opponent arranges those creatures in a pile, and then they are exiled underneath ~.
When ~ dies, put the top card of its pile onto the battlefield, and then exile the pile underneath that card without changing the order. That card gains this ability.
0/1

Criteria 2:

Order of Operations

Enchantment
Players cannot rearrange the creature cards on their battlefields after Order of Operations has been announced or while it is on the battlefield. If a creature would enter the battlefield, its controller may put it anywhere.
Each player has X consecutive combat phases on each of his or her turns, where X is equal to the number of creatures he or she controls.
Only the leftmost creature (or creatures, if they're stacked) may attack or block each combat
After each combat phase, the active player must and defending player may move his or her leftmost creature or creatures to the right of the rightmost creature on his or her battlefield.

For Criteria 2, I'm going to make a whole keyword:

Old Man George |
[Legendary Creature - Moleman Warrior]
Burrow (Play this card underneath the table. Permanents on top of the table treat this card as though it didn't exist as long as it remains under the table.)
First Strike
The whole world is his lawn, and he wants you off it.
4/3

Rules Clarification 1: Burrow only affects permanents; spells may still target permanents with burrow.
Clarification 2: If someone plays the card Enter the Dungeon, the new game begins with all burrow permanents in play as permanents without burrow.
Clarification 3: Mana produced underneath the table may be spent above the table, and vice-versa.

Battle Formations

Enchantment
When Battle Formations or another permanent enters the battlefield, each player arranges their cards in the battlefield in five columns and any number or rows.
Players can't change the columns or rows of their permanents.
Creatures can only block or target other permanents that are in the same column or in an adjacent row.

Round 2:

Curse of Ambidextriguity
Enchantment - Aura Curse
Enchant Player
Enchanted player holds their hand in the opposite hand of the hand they usually hold their hand in.
On the other hand, can one count a counter to the curse as a counter if the counter is to conduct oneself as if cursed until one is cursed? On the other hand, there are countless ones for whom handedness is no curse, but a quaint custom to cooperate with.

Round 2:

Cold Embrace
Instant (U)
Cast Cold Embrace only if you haven't moved any of your opponents' cards this turn.
Destroy two target creatures that are touching each other. (Two creatures are touching if one's card, token, or sleeve is touching the other's card, token, or sleeve.)

Goblin Drinking Game
Enchantment
Cards must be arranged in a triangle with the tip facing away from those card's controllers to the best of those player's ability.
At the beginning of each player's upkeep that player chooses target opponent. That opponent flips a coin onto that player's arranged cards. That player gains control of each card that coin lands on. If it misses that player loses 4 life.

Mixed Brain Dominance
Enchantment (U)
Whenever a player taps a permanent to the right, destroy it.