If a mode requires a target, you can select that mode only if there's a legal target available. Ignore the targeting requirements for modes you don't choose.

If an effect allows you to cast a spell with tiered "without paying its mana cost," you must still choose exactly one mode and pay the associated additional cost.

If a spell with tiered is copied, the effect that creates the copy may allow you to choose new targets. You cannot choose a new mode.

You choose the mode as you cast the spell with tiered. Once the mode is chosen, it can't be changed.

You must choose exactly one of the listed modes and pay its associated additional cost in order to cast a spell with tiered.

The mana value of a spell with tiered is determined only by its mana cost (in the upper right corner of the card). It doesn't matter which mode you choose or which additional costs you pay, including any additional costs imposed by other effects.

If you chose the Cura mode and the target permanent is an illegal target when Restoration Magic tries to resolve, it won't resolve and none of its effects will happen. You won't gain 3 life.