The trigger occurs when you use the Morph ability to turn the card face up, or when an effect turns it face up. It will not trigger on being revealed or on leaving the battlefield.
If a spell with split second is on the stack, you can still respond by turning this creature face up and targeting that spell with the trigger. This is because split second only stops players from casting spells or activating abilities, while turning a creature face up is a special action.
You don't choose the new target for the spell until Willbender's triggered ability resolves. You must change the target if possible. However, you can't change the target to an illegal target. If there are no legal targets to choose from, the target isn't changed. It doesn't matter if the original target of that spell has somehow become illegal itself.
If a spell or ability targets multiple things, you can't target it with Willbender's triggered ability, even if all but one of those targets have become illegal.
If a spell or ability targets the same player or object multiple times, you can't target it with Willbender's ability.