If Fizz is resurrected by Heedless Resurrection, can he play that same Heedless Resurrection?

To answer your question: Yes, you can use Fizz, Trickster to play the Heedless Resurrection that was used to resurrect him.

The Reasoning

This interaction is possible because of the timing of how spells and abilities are resolved:

1. The Triggered Ability: When you play Fizz, Trickster (using Heedless Resurrection), he enters the battlefield and his "When you play me" (WYPM) ability is placed on the chain.
2. The Spell's Resolution: A spell must fully resolve and move to the trash before triggered abilities caused by its resolution are processed. Because Heedless Resurrection finishes its resolution and moves to the trash before Fizz's WYPM ability resolves, it is a legal target in the trash at the moment the ability is processed.

Regarding Fizz

Fizz, Trickster has an Energy cost restriction printed on his card: "When you play me, you may play a spell from your trash with Energy cost no more than [3], ignoring its Energy cost." This restriction applies to the spell chosen from the trash, regardless of the fact that its Energy cost is ignored.

Note: I could not fully verify this ruling against the retrieved rules.