You must target two creatures as you cast Whiplash Trap. If you can't (because just one creature is on the battlefield, perhaps), you can't cast the spell.

Effects that increase or reduce the cost to cast a Trap will apply to whichever cost you chose to pay.

You can target any two creatures, not just ones that entered this turn.

Casting a Trap by paying its alternative cost doesn't change its mana cost or mana value. The only difference is the cost you actually pay.

You may ignore a Trap's alternative cost condition and simply cast it for its normal mana cost. This is true even if its alternative cost condition has been met.