This is speculation as I have not done any testing yet:
1) Yes to Wonder Labyrinth {*}.
2) No to Pokémon Communication.
Specifically, I plan on dropping one Shrine of Punishment for Wonder Labyrinth {*}. I've done something similar with a few other decks. I have noticed that Shrine too often clutters my hand, and Wonder Labyrinth {*} punishes almost every deck that Shrine does, but in a different manner, while also punishing most decks that Shrine doesn't touch. It is "passive" punishment, though, which does hurt it a bit.
Remember that this deck likes to make good use of Apricorn Maker. You can use Apricorn Maker but "fail" the search, so it cannot get stuck in hand unless you used or need to use another Supporter that turn. Great Ball, Nest Ball, and Ultra Ball are all legal Apricorn Maker targets, and can also all be "burned" (used to search but not add anything to` hand). Ultra Ball helps remove clutter from your hand. Mysterious Treasure is used in the deck even when it cannot search anything out, simple to get a card out of your hand.
Pokémon Communication can only search out a Pokémon from your deck if you shuffle another Pokémon from your hand back into your deck. You can burn it and find nothing, but you still have to toss a Pokémon back into your deck. No Pokémon in hand and it becomes a "dead" card.