You can't sacrifice a Clue to pay multiple costs. For example, you can't sacrifice a Clue token to activate its own ability and also to activate Alquist Proft, Master Sleuth's ability.

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 investigate.

If an effect refers to a Clue, it means any Clue artifact, not just a Clue artifact token. For example, you can sacrifice Wrench to pay for Alquist Proft, Master Sleuth's activated ability.

Clue is an artifact type. Even though it appears on some cards with other permanent types, it's never a creature type, a land type, or anything but an artifact type.