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.

The value of X is locked in after you choose targets but before you pay costs for Urgent Necropsy. In the extremely unusual case where the mana value of one or more of the targets changes while you're paying costs, the cost to cast Urgent Necropsy, including the additional cost, remains what you previously determined.

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