Question: How can Murphy still be alive if he doesn't have a heart?
Chosen answer: He most likely has an artificial heart or some type of system that circulates his blood, this system doesn't necessarily have to take the shape of a typical human heart. However if his biological heart is still functional, it may be behind the lungs.
Answer: Watch again the scene (s), especially close to the end when his armor is reverted to silver and just between his lungs; his heart is just behind his lungs and beating, though if you blink you might miss it.
Answer: No.