I have a lot of duels where various questions like this come up and rather than debate about it in a duel it's just easier to post here for a source to link to when needed.
Effect: Trap Cards cannot be activated. The effects of all face-up Trap Cards are negated.
Answer: Yes, Jinzo can be Special Summoned by Call of the Haunted as the Special Summon is resolved before he's officially on the field for his effect to activate. He simply negates the destruction ability afterwards of CotH's effect. So when Call of the Haunted is destroyed, Jinzo won't be destroyed.
Question: Jinzo negates all face-up Trap Cards.. then what happens with Call of the Haunted and similar cards? Can they be used to special summon him or would once summon the effect be negated and Jinzo have to be sent back to grave?
If Jinzo was special summoned with Call of the Haunted and later Jinzo is destroyed, Call of the Haunted will be destroyed.
Answer: Yes, if Jinzo is brought back with Call of the Haunted and later Effect Veiler (or a similar card) negates Jinzo, Jinzo will be destroyed when Call of the Haunted is destroyed.
Question: Well then I have a question. I negate Jinzo with... Effect Veiler or something, and destroy CotH in that situation. Does it bring down Jinzo with it?
If anyone has any other questions please feel free to ask them.