Zweischneidiges Erbstück

"Artifact" isn't a creature type.

Compare the revealed cards to the creature as it last existed before it died, not to the creature card as it exists in its owner's graveyard, to determine which one you put into your hand.

If Heirloom Blade leaves the battlefield at the same time that the equipped creature dies, its triggered ability triggers.

If the equipped creature has no creature type, no card can share a creature type with it.

If you don't reveal a creature card that shares a type with the creature that died, you'll just reveal and randomize your library.

You'll reveal cards until you find one that shares at least one creature type with the creature that died. For example, if a Cat Wizard dies, you'll stop if you reveal a Human Wizard or Cat Soldier.