If you sacrifice a permanent as part of a spell or activated ability's cost, Korvold's last ability will resolve before that spell or ability.

If you sacrifice Korvold, its last ability triggers. You won't put a +1/+1 counter on anything, but you'll draw a card.

A legendary permanent that is put into a graveyard because of the "legend rule" isn't sacrificed.

Korvold's last ability is a triggered ability, not an activated ability. It doesn't allow you to sacrifice a permanent whenever you want; rather, you need some other way of sacrificing permanents, such as Korvold's first triggered ability.

If you somehow control no other permanents, you can attack with Korvold. You won't sacrifice anything, and there's no penalty for being unable to do so.