From Fizz's skill description it says he is untargetable upon the initial use of E. If he chooses to jump again, for example through Veigar's Event Horizon, does he remain unaffected or will he be stunned?
When Fizz jumps over Veigar's Event Horizon he will jump through it but end up stunned in the middle of the ability. I just tested this with a friend.
Yes, The stun is based on barrier collision.
Fizz's playful/trickster is a skill that makes him untargetable. Use any skill that channels or is an area of effect skill. He won't be able to evade these unless he jumps out of the area that is being affected.