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.

Some spells and abilities that investigate may require targets. If each target chosen is an illegal target as that spell or ability tries to resolve, it won't resolve. You won't create any Clue tokens.

Eliminate the Impossible affects only creatures your opponents control at the time it resolves. Creatures they begin to control later in the turn won't get -2/-0 and won't stop being suspected.

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.

If a suspected creature loses all abilities, it will lose menace and "This creature can't block", but it won't stop being suspected.

There's no limit to the number of creatures that can be suspected simultaneously. Suspecting a new creature doesn't cause other creatures to stop being suspected.

When an effect suspects a creature, it becomes suspected. It gains menace and "This creature can't block" for as long as it's suspected. It stays suspected until it leaves the battlefield or another effect causes it to no longer be suspected.

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.

Some abilities trigger "whenever you sacrifice a Clue". Those abilities trigger whenever you sacrifice a Clue for any reason, not just to activate a Clue's activated ability.

If a creature is already suspected, suspecting it again won't have any effect.

Being suspected isn't a copiable value. If a permanent becomes a copy of a suspected creature, it won't be suspected.