At the moment Shadar Haran is still a mystery. But that makes him all the more interesting. First lets take a look at what we know for sure about him:

He is definetly not a normal myrdaal. His height is the first givaway, so far all the fades we have seen so far seem to look identical. Also we have his ability to "smell" the difference between saidin and saidar, he thinks to himself that no other fade can do this. He also apparantly can do something close to channeling, examples of this are his burning of a spear to ash in the scene after Sammael and Graendal scatter the Shaido using gatways, also he can block channelers from the power (as seen with Osan'gar, Aran'gar, and mogheden). He can create a dark ball of something that casts a strange light. Also Shadar has a sense of humor something that the forsaken have never seen in a fade before.The last physical differance i can remember is his inability to stay away from shayaol'ghul, this has never been mentioned of any other fade so we can assume it is unique to Shadar Haran.
His standing with the dark one is higher than any other myrdraal in history. Its not clear yet exactly what his position is, however weve seen that he orders around forsaken with out fear (prior to this the only ones the forsaken have had to obey was the DO himself.) So its safe to assume that he is higher than regular fades and darkfriends. The only charactor who might tbe his equal or superior is moridin, But since we havent seen them interact or think about each other we have to guess. (more on this later)
He is either very smart or has someone telling him what to do who is. The fact that none of the good guys know about him is evidence of this. Many Forsaken have died because of Rand and his friends so its clear they are a threat. And since its hard to kill someone you dont know about he is safe for the moment.
He does think for himself as shwon by his desire to desire to change whatever makes him unable to stay away from SG for lng periods of time. Thats not much to go on but if we read closely we can figure out a lot about him. First since none of the forsaken have ever seen anything like him its probably not some kind of mutation or birth defect, since the myrdraal have been around for more than 3000 years it most likely would have turned up at least once. That leaves either human intervention, again unlikely since Aginor was the only forsaken who was capable of such a thing (he created trollocs and myrdraal even if the myrdraal werent intentended) and he apparenly attacked and was killed by Rand and crew almost immediatly after being freed, and Shadar Haran was around before he reincarnated as one of the gars. All of the Forsaken are skilled in different areas without much overlapping apperantly and none of them has been mentioned as having any skill in biology og genetics. Or something done by the DO himself. This i think is the most likely origin of the super fade. Why you might ask? Simply because he needed someone e he could trust. All the Forsaken have pretty much done their own thing since being freed and are dropping like flies. Even Ishamael the DO's golden child went nuts in the end and tried to kill Rand at the stone of tear. Maybe The DO thought that a fade would have more common sense, but whatever the reason Shadar Haran was created. So far he seems to be acting as an enforcer for the dark one, bringing all the forsaken under control by whatever means necassery. But that raises another question since he seems to be handing that control over to moridan ,who is now nai'blis. The question is: is he moridans henchman, superior, or equal? At first one might think that he is working for moridan because he does seem to be doing moridans dirty work (ie "rehabilitating moghedan and convincing graendal that moridan is nae'blis) but i dont think so. My theory is that Shadar Haran and Moridan are equals, and its Shadar Harans job to bring every one under control and keep them there while Moridin does all the planning and organizing. Also when Shadar Haran identifies himself he say that he speaks for the DO and that anything he says can be considered the DO's word. To me that sounds like he doesn't recognize anyone above him in the darkfriend/forsaken heirarchy. The only thing that is clear about Shadar Haran is that he will be a very dangerous opponent and a key player in deciding the fate of the WoT world.