I guess you mean psychopaths, Sociopaths are anti-social, so my guess is they are not charming. It's a generalization but you do not get to the top without being persuasive at decent level and to stay there, you better be good.
You've got it backwards. Psychopathy is a particular variant of Antisocial Personality disorder and is characterized by a complete lack of empathy. The brain wiring literally doesn't exist.
Whereas sociopathy is a learned willingness to completely subvert empathy to serve personal goals. They do have brain wiring for empathy, which is what makes them effective at subverting it.
High-functioning psychopaths generally have to create a 'mask' in order to pass for normal. The mask is quite cognitively expensive and so they tend to prefer solitude. Low-functioning psychopaths tend towards criminality due to poor self-control.
You’ve got it reversed. Sociopaths lack empathy, but are not anti social. Instead they use manipulative social interaction like a knife to get what they want. Psychopaths are just crazy in comparison.