Ispettrice di Vitu-Ghazi

If the target creature is an illegal target as Vitu-Ghazi Inspector's triggered ability tries to resolve, it won't resolve and none of its effects will happen. You won't gain life.

If you can't exile enough cards to meet or exceed the required mana value, you can't choose to collect evidence at all.

Once you've announced that you're casting a spell, players can't take actions until you've finished doing so. Notably, opponents can't try to remove cards from your graveyard to stop you from collecting evidence.