I play Heedless Resurrection and kill my Fizz as additional cost. Can I resurrect that Fizz for the Heedless?

No, you cannot resurrect the same Fizz you killed to pay the cost.

Why: When playing Heedless Resurrection, targets are chosen before costs are paid (step 2 of playing a card). Fizz is still on the board at that point — not in the trash — so he's not a legal target. By the time you kill him as the additional cost (step 4), the target choice is already locked in and cannot be changed (Rule 355.15). You'd need to pick a different unit already in your trash.

FAQ #9523 confirms this ruling directly.