You can play Misty & Lorelei for the base effect as long as there's at least 1 card in your deck. You can always play it by discarding 5 cards from your hand.
Source:
Cosmic Eclipse FAQ (2019-10-18), TPCi Rules Team (2019-10-31)
You can play Bellelba & Brycen-Man as long as there's at least 1 card in either player's deck. It can also be played by discarding 3 cards from your hand if at least 1 player has more than 3 Benched Pokemon. But if at least 1 player doesn't have more than 3 Benched Pokemon, you cannot discard cards from your hand.
Source:
Cosmic Eclipse FAQ (2019-10-18), TPCi Rules Team (2019-10-31)
When I use Roxie to discard two Pokemon that each have the "Blow-Away Bomb" Ability, do those abilities stack so I can place two damage counters on each of my opponent's Pokemon?
Yes, each of the Pokemon gets to use their own "Blow-Away Bomb" Ability when discarded by Roxie.
Source:
Cosmic Eclipse FAQ (2019-10-18), TPCi Rules Team (2019-10-31)
You can play Cynthia & Caitlin as long as there's a Supporter card in your discard pile. You can also play it by discarding a card from your hand if there's at least 1 card in your deck. But if you have no cards in your deck, you cannot discard a card from your hand.
Source:
Cosmic Eclipse FAQ (2019-10-18), TPCi Rules Team (2019-10-31)
When I play Guzma & Hala, after I search my deck for a Stadium, do I have to shuffle first if I'm also going to search for Special Energy and a Tool?
You can skip the shuffling after the Stadium search as long as you clearly tell your opponent you're doing the second part of the card. So if you're doing both parts you first discard two cards from your hand, then search for any Stadium you're going to take, then search for the Tool and Special Energy, then shuffle your deck.
Source:
Cosmic Eclipse FAQ (2019-10-18), TPCi Rules Team (2019-10-31)