Say Team Magma's Secret Base and Mimikyu with "Shadow Box" Ability are both in play. If I put Dedenne GX on the Bench, can I use its "Dedechange" Ability or will it be blocked because it has damage counters on it?
Since Dedechange and Team Magma's Secret Base are simultaneous effects, it is up to the player to choose the order in which they will be applied.
Source: TPCi Rules Team (2021-04-08)
Can you use the "Dedechange" Ability when you play Dedenne GX from your hand while Power Plant is in play?
No, you cannot. Dedechange does not activate until Dedenne GX is on the Bench, at which time it is considered "in play" and therefore blocked by Power Plant.
Source: TPCi Rules Team (2019-08-22)
For Dedenne's "Dedechange" Ability, can I use it if I have no hand to discard?
Yes, you can. A hand of zero cards is still a hand, so you would discard nothing and then draw six cards.
Source: Unbroken Bonds FAQ (2019-04-19), TPCi Rules Team (2019-05-02)