Sram'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.

While you're casting your free spell, the Expertise spell is still on the stack. It will be put into its owner's graveyard after the free spell is cast. The free spell can't target the Expertise card in your graveyard. It can target the Expertise spell on the stack, but the Expertise spell will become an illegal target before the free spell resolves.

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.