When my opponent has Goodra with the "Slimy Room" Ability in the Active Spot, if I try to attach an Aurora Energy to one of my Pokemon and I flip tails, do I have to discard a card for the cost of Aurora Energy too?
No, since the flip happens before it is attached, if Aurora Energy is discarded you do not have to discard another card along with it.
Source: Fusion Strike FAQ; TPCi Rules Team (2021-11-11)
If my opponent has Goodra with the "Slimy Room" Ability in the Active Spot, do I still have to flip a coin to attach an Energy to one of my Pokemon that already has a Fusion Strike Energy card attached to it?
Yes you still have to flip a coin, because the Slimy Room Ability is acting on you the player not on a specific Pokemon; and Fusion Strike Energy's effect applies to the Pokemon it is attached to, therefore it does not block Slimy Room's effect.
Source: Fusion Strike FAQ; TPCi Rules Team (2021-11-11)
While Goodra's "Slimy Room" Ability is active, if I use an Ability or card effect like Swampert's "Muddy Maker" Ability to attach an Energy card from my hand but flip tails, can I use that ability or effect when I try again with another energy?
No. The Ability has been used and the energy is discarded even though your regular Energy attachment for the turn has not been used up.
Source: Fusion Strike FAQ; TPCi Rules Team (2021-11-11)
While Goodra’s “Slimy Room” Ability is active, if I try to attach an Energy card but flip tails and have to discard my energy instead of attaching, can I try again?
Yes, as long as you can get another Energy card in your hand.
Source: Fusion Strike FAQ; TPCi Rules Team (2021-11-11)