How did Kourin copy Aichi's deck? In Season 1 Episode 6 - "The Mysterious Card Shop!", when Aichi fights Kourin, Kourin appears to have duplicated Aichi's Royal Paladin Deck.

In Episode 23 - "Fateful Encounter" it was the same in the match between Kourin and Ren however Ren was invited to PSY and Kourin had Ren play using a pre-built deck which was the same she used. as Ren noticed it was because Kourin was seeing a person's true skill as a fighter rather than the strength of their deck.

But i don't recall Aichi, Morikawa or Izaki being invited to PSY rather they found it by accident and even if they were invited, unlike Ren, Aichi had never been in any tournaments so there was really no way for Kourin to know what was in his deck via any broadcasts.

So how did Kourin copy Aichi's deck?
Aichi and Kourin had very similar decks but they were not identical. For example, Kourin is seen to have a Stardrive Dragon, which Izaki and Morikawa remark earlier in the episode is 'legendary' and not available or easy to find anymore. Aichi is never seen to play this card. She also uses Crimson Butterfly, Brigette, which again is a card that Aichi never plays. Despite Kourin having cards like Wingal that appear to exclusively support Aichi's Blaster Blade, she is never seen to use one herself.

I believe the main purpose of Kourin and Aichi's first cardfight was to establish that even with similar decks, their skill and play styles are very different. Kourin does not appear to have deliberately copied Aichi's deck.

In episode 23, I believe you are correct. Kourin and Ren use pre-built identical decks to judge Ren's skills without access to his usual cards.