Sociopaths very much have the ability to feel, it is key to our ability to understand the emotions of our targets. The difference is our ability to turn that off when needed. To disassociate ourselves from those emotions when it is to our benifit to do so. A great actor cannot portray and emulate emotion properly unless they can in a sense, feel it themselves. This is criticial to our ability to manipulate others.
The concept is easy to master, even for an empath such as yourself. It is nothing more than learning to view yourself from the outside. Seeing yourself as if you are watching yourself on TV... an actor in a tv drama. You can choose not to empathise with this charector, just as you can choose to or not to empathise with the charectors in your favorite tv show. It's all quite zen actually... to disconnect from yourself.
For further reading on this topic: http://www.bbc.co.uk/news/science-environment-23431793
As to whether you can be a sociopath and not exhibit all of hares traits: http://en.wikipedia.org/wiki/Hare_Psychopathy_Checklist#The_two_factors
The answer is no, you do not need to qualify on every trait to be diagnosed. Infact some would argue that we all fall on the spectrum of sociopathy to varying degrees.
And disregard what people are saying here. I assure you, I browse this forum quite often. ;)