The Demon behind Nero is Sparda the Dark Knight(or Black Knight). He was a demon general with great reputation who stood up for humanity when humanity tried to resist the invasion of the demons. Sparda fought his kind to help humanity and that is why humanity praises him. The reasons why he did this are speculative and indicate to Dante falling in love with a human(most likely Nero's mom). As to why do Nero, Dante and Virgil look alike, they look alike because they are brothers and all sons of Sparda in some way. Dante and Virgil are full fledged demons and sons of Sparda probably through some demonic relationship while Nero seems to be a half-demon (the demon arm he possesses might be proof of this) indicating that Sparda might have had some sort of human lover, Nero's mother.
Actually, Dante and Virgil are twins born of Sparda's union with a human maiden. Dante and Virgil are thus, Half-Demons.
It is plausible that the demon behind Nero in his DT form is Sparda, but it's more likely that it's Virgil's Devil-Trigger form (It has the same design, the katana sheath housed parallel to the arm, etc.). Sparda used the Force-Edge, not the Yamato.
I don't think Nero is related to Dante or Virgil, but rather Capcom didn't want to break away from the "Sexy, suave, stylish white-haired part-demon who uses huge swords" theme for the main characters. Smart move on their part too.
i didn't play through the whole game (yet) but as i understood it Nero resurrected Virgil's power thus receiving the demon arm if u watch through scene when Nero gets Yamato and unlocks his DT form (and a scene afterward when all those bad guys have a meeting with His Hollyness) u should hear it all