You can't activate Deadeye Tracker's ability without targeting two cards in a single opponent's graveyard.

If one target card is an illegal target by the time Deadeye Tracker's ability resolves, the remaining legal target is exiled and Deadeye Tracker explores.

If each target card is an illegal target by the time Deadeye Tracker's ability resolves, the entire ability is countered. Deadeye Tracker won't explore.

Once an ability that causes a creature to explore begins to resolve, no player may take any other actions until it's done. Notably, opponents can't try to remove the exploring creature after you reveal a nonland card but before it receives a counter.

If no card is revealed, most likely because that player's library is empty, the exploring creature receives a +1/+1 counter.

If a resolving spell or ability instructs a specific creature to explore but that creature has left the battlefield, the creature still explores. If you reveal a nonland card this way, you won't put a +1/+1 counter on anything, but you may put the revealed card into your graveyard. Effects that trigger "whenever a creature you control explores" trigger if appropriate.