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)
When I play Guzma & Hala, can I discard the Stadium I searched for as one of the 2 cards discarded to search for the Tool and Special Energy?
If you want to do the second effect you have to discard 2 cards "when you play this card", that is before you search for the Stadium.
Source: Cosmic Eclipse FAQ (2019-10-18), TPCi Rules Team (2019-10-31)
You can do any part of Guzma & Hala as long as there's at least 1 card in your deck.
Source: Cosmic Eclipse FAQ (2019-10-18), TPCi Rules Team (2019-10-31)