Question about Master of predicaments

[potimusprime]

Hi there thanks for taking the time to read this, im hoping to find answers to two questions. The first of which is, if i were to deal damage with Master of Predicaments, choose a card and my opponent guesses wrong, I can now play said card without paying its cost, can my opponent cancel that card?  Second question I think I already know the answer to but I just want to be sure. I have a Lazav, Dimir Mastermind and I copy a creature that has an ability that is triggered by it entering the battlefield does that ability get triggered? I assume it doesnt since lazav is already on the field and its just copying a creature.

[Cheddarchet]

To answer your first question: Yes, it can be countered, since you're still casting the spell as you would normally. There's just no cost.
And you were right on the second one. Since Lazav is already on the field, no ETBs would trigger.