Yahenni's Expertise

The mana value of a split card is determined by the combined mana cost of its two halves. If an expertise spell allows you to cast a split card, you may cast either half or, if that split card has fuse, both halves.

Any triggered abilities that trigger while performing the Expertise spell's first effect won't be put onto the stack until after you're done casting your free spell. They're put onto the stack at the same time as any abilities that triggered while casting that spell regardless of the order in which those abilities triggered.

If a creature's toughness is reduced to 0 or less by Yahenni's Expertise, that creature is still on the battlefield as you cast your free spell. It can be the target of that spell, although it will become an illegal target before that spell resolves. If it has any abilities that trigger on the spell being cast, those abilities will trigger.