The first is incorrect -- see @gotube's excellent comment for details.
The other two are (again, as @gotube commented) fine, but have slightly different nuances. The first could be leaving it open that the person from whom we're expecting to hear might not contact us. It might even be used as a euphemism, and is actually a demand, or plea that they do contact us. So, perhaps I'm an accounting clerk, calling up a customer who is late paying a bill. They tell me they are sorry, and that they will send the check very soon. I end the call with:
Well I advise you to do so, otherwise we'll have to send this to debt collection. I look forward to hearing from you.
The third does not have that nuance. The speaker really is simply "looking forward" in a positive way to future communication that they expect will happen.