Joking aside, even if this were running to the literal ground, it would probably still be wired incorrectly. As I understand it, ground is supposed to be bonded to neutral at the service. Running ground to the earth could end up being dangerous.
I'm not an electrician, though. If you aren't either, you should get one to at least check your setup.
Naah, it's actually both. Like other said, you wire ground to neutral, so in situation where metal body of any machine gets into contact with live wire your fuses break instead of killing you when you touch it. However you also have to think about electrostatic buildup from the environment which is why you have rod planted into the ground.
If it isn't eventually connected to the actual ground then it isn't a real ground wire. It's a failsafe path so technically hot / neutral by themselves are sufficient for things to work but yes, ground should connect to the Earth. It's just usually at a single point near where the utility company has their meter.
Both neutral and ground are eventually connected to earth, to prevent lightning strikes from causing destruction on the rest of the grid (and, as far as I know, there's no other need for earthing). But the "ground" circuitry in your home should never be connected to earth. The whole point of having a ground is so that if metal casing becomes hot, the easiest path is back through a circuit breaker. If you connect your ground circuit to earth, it can bypass the breaker and hurt someone.
Again, not an electrician, consult a professional, etc etc.
The neutral is supposed to go into your electricity provider without touching anything, but the ground is supposed to be grounded as often as you need.