Devil Arms are typically powerful weapons created from demons, usually seen as melee weapons (with some exceptions like Pandora, Geryon, and the Doppleganger). Unlike Dante, Nero never uses any Devil Arms, but it isn't necessary because he literally has a devil arm.
In-universe, Nero is named after the black blanket that he was wrapped with when he was found outside of an orphanage, as the word "nero" means "black" in Italian. However, there are other things that imply Nero being named after the Roman emperor:
Credo, Agnus, Sanctus, Kyrie, and Gloria from 4 are all named after the different parts of the Roman Catholic "Ordinary of the Mass". Their naming actually makes a bit of sense. Nero was a Roman Emperor well known for persecution of Christians, and the Order, with whom he is in conflict with, are all named after elements of the church. In 4, Nero is the "rebellious" member of the Order of the Sword, he doesn't actually adhere to what they're worshipping, he's just there for Credo and Kyrie.
Emperor Nero was widely believed to have started the Great Fire of Rome. DMC Nero's signature weapon, Red Queen, has an Exceed system that ignites the sword with flames.
Also, all of the aforementioned Order of the Sword characters (Credo, Agnus, Sanctus, Gloria) who use demonic power have names that are Latin words, as opposed to the odd man (well, woman) out, Kyrie, which is a Greek word.
The legends of Sparda state that he fought against legions of demons by himself. A difficulty mode in 4 actually allows you to fight of legions of demons by yourself. The name of said mode? Legendary Dark Knight. (Bonus points if Dante is using the Sparda costume)
Vergil's moveset in 4 is much flashier than before. However, considering that his story in 4 takes place before 3, it makes sense that he was not as precise then, even needing the Summoned Swords to help him perform Trick. Vergil hasn't perfected his Darkslayer style at that point in his life. The Concentration Mechanic is basically proof of this.
Also, notice how some of his moves (namely Yamato Combo C) have him wildly flailing Yamato. Hell, he straight up borrows some of Dante's moves (Kick 13, Million Stab, etc.).
In 4, Nero could (theoretically) use Devil Bringer to save Kyrie on at least two occasions. However, the only things you use the Devil Bringer for in-game is as a grappling hook against non-corporeal targets or to lay the smackdown on the bad guys, neither of which requires a delicate touch. Perhaps the Devil Bringer is incapable of being used in a gentle manner?
Also, rewatch the cutscene in which Kyrie first sees the Devil Bringer. Nero tries to hide it behind his back, which would be hilarious if it weren't so tragic. He doesn't even want her looking at the mark of his curse (as he sees it), let alone coming into contact with it. It was no accident that the final cutscene of the game had Kyrie interlacing her fingers with those of the Devil Bringer - it was the ultimate sign that she had accepted Nero for who he was.
In the second Nero vs. Dante battle, Nero's final attack is identical to the one Vergil used in 3 to defeat Dante. However, Dante stops Nero as he has become more skilled. Although it is ridiculous that Nero would know Vergil's attacks, it could have been made to hint that he really is Vergil's son.
As well as showing that Dante has learned from his fight with Vergil, and won't fall for the same trick twice.
One peculiar trait of Nero in 4 is that he swings Red Queen around with just his left hand for a majority of his attacks. It seems like a pretty odd way to make him distinct from Dante. However, it may have served as a subtle connection to another character. Earlier in 3, Vergil is shown wielding another BFS of the series, Force Edge, with one hand. Considering that Nero seems very similar to Vergil, perhaps this was done to further establish some relationship between them.
There's also the fact that his right hand started in a sling and ended up a demonic claw, he might just be using his left hand to swing Red Queen and fire Blue Rose since it's still human and easier to use them.
It gets even better on the few occasions Nero wields both Red Queen and Yamato at the same time. What other character in the franchise has been shown to use a similar combat style?
Dante letting Nero keep Yamato; by most laws of inheritance, a deceased person's possessions go to any offspring before sibling. So as Vergil's son, Yamato rightfully belongs to Nero, not his brother Dante. Dante knows this and is just using It Was a Gift as a convenient excuse to give it to him; Nero's not quite ready to learn who his dad was and it avoids the subject for a while.
It's kind of brilliant how the three each have different demonic forms based on their interpretation of Sparda. Credo and Agnus both see him as a holy savior so they have light colors, and while Credo takes a purely angelic form as he sees Sparda as an Ascended Demon, Agnus' takes an insectoid form similar to how Sparda's wings actually looked. Compare and contrast Sanctus, who fully acknowledges that Sparda is a demon and grows horns for the final boss fight.
In the case of a song having a meaningful name upon analysis, the track that plays over 4's ending, "La Vita Nuova," takes its name from the collection of Courtly Love poetry written by the historical Dante. This works on a number of levels: first, the song plays over the start of Nero and Kyrie's new life together; second, Kyrie's acceptance of Nero as he is marks the signing and sealing of their love in a way that the Dante of the poems could not attain; third, as was common in Courtly Love poetry, the love being celebrated brings the protagonist closer to the divine.