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You may still have to package the cards, but thats often as far as it goes

In the current state of the game, mill decks, stun decks, stall decks, and regular decks are all viable options

Yes, you can counter a triggered ability with specific cards that say counter target triggered ability. Regular counterspells like Counterspell only work on spells, not abilities already on the stack

Abilities that trigger "when [that creature] connives" will trigger.

To make better use of the heal mechanics with reducing strength, think about Vanellope von Schweetz Sugar Rush Princess and Vanellope von Schweetz Candy Mechanic as a Shift target that does the same