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?
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?