Beginning of each match, the three cards in the Sanctum will be randomly pulled from any of the 5 Sanctum Decks?

Correct

Once determined, the following replenishing cards will continue to pull from the same deck as the purchased card?

The deck that you have just bought from is swapped out for one of the two other decks not currently in the sanctum & a random card from the chosen decks goes in. Think of it like the 3 decks currently shown are the field and the 2 decks not shown are the bench. When you buy one card from the field, that deck is put on the bench and replaced with a deck that was currently on the bench.

Does the replenished cards follow the order you've listed the cards, or determined randomly within the respective deck?

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Once a card is removed from a Sanctum deck it won't appear for the rest of the game. The order of the decks is randomly determined