Question: How can Murphy still be alive if he doesn't have a heart?
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.
Except the heart is located in front of the lungs, not behind them.
Why Murphy's heart isn't where it should be in a normal human is up to speculation-perhaps the transformation into a cyborg necessitated it's being repositioned, perhaps. The heart is there, though.
Normally, yes, but who's to say they didn't have a reason to move it behind his lungs when they rebuilt him?
Question: Many times, when Robocop's helmet screen is not in front of his eyes, he can still get and see information about people. How come?
Answer: The helmet doesn't contain a screen - it's purely there as protective armour. Murphy's heads-up display is built directly into his eyes.
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.