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.

Surveillance Monitor's last ability triggers whenever you collect evidence for any reason, not just when you collect evidence with its first ability.