Is that meant to happen?
It works fine. If you’re using a foretell card that goes to your hand when its gem is destroyed (a spell or support), maybe you’re running into the issue where Korvold’s draw happens first. If it fills your hand, you won’t get the foretold card.
Yep, you have to make sure you have room for two cards in hand. One for the draw, and one for the foretold card.
Keep in mind he also destroys other token supports. For example, Bolas3’s first loyalty ability support.