That picture you posted looks like some type of shock or tilt sensor, its hard to tell for sure from the picture.
If an alarm is still installed, and you have no way to arm or disarm it, you have a couple of choices. You can just leave it alone and hope there is never a malfunction. You can try to find out what brand/type it is and see if there are replacement remotes available. Or, you can attempt to remove it.
Is it currently causing you any problems? If its all still there, you can usually find the main control unit stuffed up under the driver's side dash somewhere. There will be quite a few wires that terminate there. If it doesn't present itself upon initial inspection, you could always trace the wire from that LED back. It should lead you straight there. If you decide to try to remove it, I recommend only doing it yourself if you have experience with alarms, car electronics, and a multimeter. Depending on the alarm and installed options, removing it without some knowledge could leave your car immobilized.
As far as that antenna, I would say yes, it has a better chance of being something like a partial cell phone antenna than anything to do with the alarm.