In MoI (?) it is stated that he is human and he gets his immortality from smoking those candles. His curse was that he'll fail at everything he ever tries to achieve (going purely off memory here) ... if his immortality is conferred by the curse as you suggest, then what was that with the candles?
Regardless of whether he is or is not human, the question still remains: where does he get his power from? He is not a dragon, a Jaghut, a Tiste, a K'Chain che Malle, an Imass, or a Forkrul Assail. So what is his magic, and where does it come from? This is one of the problems with Malazan, in my opinion. Supposedly, all magic comes from either the Elder warrens or their accessible-to-humans derivatives, or from an alien source, such as The Crippled God. Yet we have someone like Kallor striding across the landscape like one of the super-powered beings, with no explanation of where his power comes from and how his magic works. There is very little logical consistency in Malazan, in my opinion, which is why so many fans find it incomprehensible rubbish.