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.

If either target is an illegal target as Bite Down on Crime tries to resolve, the creature you control won't deal damage.

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