You surveil 1 even if the opponent doesn't discard a card, perhaps because they had no cards in hand at all.

Some spells that instruct you to surveil require targets. You can't cast a spell without choosing legal targets. If all of those targets become illegal, the spell doesn't resolve and you won't surveil.

You perform the actions stated on a card in sequence. For some spells and abilities, you'll surveil last. For others, you'll surveil and then perform other actions.