Mayhem Patrol

If you choose to pay the blitz cost rather than the mana cost, you're still casting the spell. It goes on the stack and can be responded to and countered. You can cast a creature spell for its blitz cost only if you could cast that creature spell. Most of the time, this means during your main phase when the stack is empty.

If you pay the blitz cost to cast a creature spell, that permanent will be sacrificed only if it's still on the battlefield when that triggered ability resolves. If it dies or goes to another zone before then, it will stay where it is.

The triggered ability that lets its controller draw a card triggers when it dies for any reason, not just when you sacrifice it during the end step.