Nero heard vergil voice in his head but it was probably an allucination made by Yamato , it wasn't vergil himself but I think it was his sword that talked to Nero
I think that Yamato is anxtention of vergil himself like the sword dante is for Dante
since vergil doesn't even know about his son and does realize of the fact that he had Yamato only a few years after I doubt even vergil himself know about that
Also I don't think That the devil bringer is a piece of vergil soul but it's a demonic part of Nero... Nero seems to transform when he proves a strong emotion, when that day kyrie was attacked he needed more power but wasn't able to completely unlock his devil trigger so he unlocked only a part of it the devil bringer... When vergil and Dante were in danger in dmc 5 he was finally able to fully achieve is devil trigger
I hope the developer pointed this out in later game since they didn't explain that part, and didn't explain how Yamato was even broken