Can I combine ground and neutral wires before they connect to their bus bars?
No, you can't do that because a single fault would make it deadly.  Consider what would happen if the combined neutral+ground wire came loose in your panel -- all the current that was trying to return via neutral wouldn't make it, and instead it'd be able to flow back along the ground wire, energizing the chassis of your appliance with 120V.  On the other hand, if they're separate wires all the way to the panel, either one coming loose won't create a safety issue.  What you can do instead is put a junction box next to your panel, as far as the current wires reach, then splice to a short length of new wire to get the needed reach.  
You shouldn't put two wires on the receptacle screw unless it's meant for that, and it's probably not.  A better way of doing it is to pigtail the ground to the receptacle: wire nut the box ground, the receptacle ground, and the incoming ground wire from the panel together.