What is the relationship between Alejandro (played by Benicio Del Toro) and Fausto Alarcon (played by Julio Cesar Cedillo) in Sciario?
I know that Alejandro is a laywer - was he a lawyer for the cartel or an opposing cartel?
Alejandro was a prosecutor in Juarez for the Mexican state (essentially a district attorney) who was targeted by Alarcon and the Sonora cartel for reasons that are not specified, but in all likelyhood he and his family were picked on for possibly nothing more than him doing his job.
It is only after the tragedy that befell him that he appears to have offered his services to the Medellín cartel and subsequently the CIA in order to exact revenge on Alarcon, as Alarcon challenges Alejandro about the change in his nature (acting as a 'Sicario') just before Alejandro slaughters him and his family.
Sicario The day of the soldado shows Alejandro gunning down a high ranking lawyer representing a cartel. But before executing the lawyer, Alejandro takes off his mask in the middle of what seems to be a very upscale business district probably riddled with security cameras. It seems Alejandro wants the lawyer to recognize him despite putting him at risk of being identified by law enforcement. This leads me to believe that this lawyer must have had something important to do leading up to Alejandro's family being murdered. We know Alejandro was a prosecutor for the state and Perhaps the lawyer offered to bribe Alejandro to drop charges against cartel activity or even relayed threats from the cartel bosses.
The point is, Alejandro must have worked on a few or at least one major case against a cartel, most probably Sonora cartel of which Fausto is a high ranking boss. To back Alejandro down or to hurt him for winning a case against cartel or not listening to the cartel, Fausto seemed to have directly ordered Alejandro's family killed. The dialogue at the dinner table suggests that Fausto and Alejandro probably hadn't met in person before but definitely knew about each other.
So in short, Fausto was a cartel boss who had Alejandro's Wife's head cut off and his daughter put in a vat of acid for bringing legal trouble to the cartel while Alejandro was a prosecutor for Juarez, Mexico.