No, counters of any kind stay on a transformed card
Whether or not your cards are expensive, they're precious
You need: Three Hoothoot (Temporal Forces, 126) Three Bouffalant (Stellar Crown, 119) Two Noctowl (Temporal Forces, 127) Two Terapagos ex (Stellar Crown, 128) Two Snorlax (Lost Origin, 143) One Lumineon V (Brilliant Stars, 40) One Fezandipiti ex (Shrouded Fable, 38) One Noctowl (Stellar Crown, 115) One Fan Rotom (Stellar Crown, 118) One Radiant Greninja (Astral Radiance, 46) The Bouffalant help to mitigate damage, while Fan Rotom, Radiant Greninja, and Lumineon V make finding specific cards to set up with a lot easier
Will you be including it in any of your decks
In the earliest days of the game, Trainer cards had no restrictions on their use, so with the maximum 4 copies allowed in the deck, a player could draw 8 extra cards in one turn if they were all in the hand during the same turn
So there will be no exchange at all