If I play Fizz Trickster, can the spell he casts target him?

Yes, a spell cast by Fizz, Trickster can target him, provided the spell's own targeting requirements allow it.

According to Rule 355.9.c: "An ability of a permanent can target that permanent, because abilities and their sources are separate objects." While Fizz's ability is the source that allows you to play the spell, the spell itself is a separate game object. As long as the spell you choose from your trash has targeting criteria that Fizz meets (e.g., "Target a unit"), he is a legal target for that spell.

Important considerations:

• Targeting: You must declare the target when you play the spell from your trash (Rule 355.10).
• Power Cost: Even though Fizz allows you to ignore the spell's Energy cost, you must still pay its Power cost (as stated on Fizz's card).
• Fizz's Ability: Fizz's ability is a "When you play me" triggered ability. It uses the chain. You play the spell as part of the resolution of that triggered ability.
• Legality: Ensure the spell you choose does not have a restriction that would exclude Fizz (e.g., "Target an enemy unit" would not allow you to target your own Fizz).