Rules question:

Rules question:

Rules question:

TLDR:  Does a spell prepared as though it were lower level count as the original level or the modified level for effects that count the level of a spell?

I am a wizard who takes Prodigy: Invisibility, such that I prepare Invisibility as though it were level 0 (I assume this is a legal move, as Prodigy does not forbid it and 0 is one less than 1).  There are a few different scenarios that I am confused about.

I am level 3, and I have taken Arcane Ward.  I prepare my cantrips (0), Invisibility (0), Magic Missile (1), and Fireball (3).  I cast and forget both Magic Missile and Fireball, so that I only have Invisibility and my cantrips prepared.  Is Arcane Ward active?

I am an arbitrary level, and I have prepared Invisibility (0) and a variety of other spells.  I cast Invisibility.  I am hit by a blind-fired arrow while invisible, and I use Spell Defense to end my Invisibility and negate damage.  Do I negate 0 damage or 1?

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Now consider instead that I have taken Prodigy: Mirror Image.

I am level 6, and I have taken Spell Augmentation.  I have prepared Mirror Image (2), Fireball (3) and a variety of other spells.  I cast Mirror Image.  I cast Fireball on a creature.  I use Spell Augmentation to end my Mirror Image and add damage.  Do I add 2 damage or 3?