''The idea of Vergil is Nero's father is sorta obvious. I mean the Yamato accepted him. and it reacted to his arm. and Nero in D.T is actually his soul, which feels similar to Vergil's, as stated by Dante.''
First off, the sword didn't react to his arm, all we saw was that Nero tried to grab the Yamato with his arm, he put all his strength into it. The arm so far has no reason to be connected to Vergil, it's just Nero's arm and it has the power to interact with demonic things. That's it.
Also, Nero doesn't have to be Vergil's son to be able to react to the Yamato. Everyone who has Sparda's blood can react to the Yamato and use it. The Yamato didn't accept him, Vergil's soul did, and his soul is inside the Yamato. Vergil called out for more power, Nero wanted that too, and so they entered into a pact. For all we know, if Dante were the first person to have found the Yamato, he might've been able to channel Vergil's soul somehow too. But I think the reason why Nero was able to and Dante later can't, is because Nero was badly wounded and was about to gain the devil trigger. It's possible that the only way for Vergil to 'resurrect' (so to speak) is to create a devil trigger inside somebody who had not gained a devil trigger yet, or to go into devil trigger himself in unison with that person (which he did with Nero).
There's still no proof that Vergil is Nero's biological father. Everybody loves bringing up this art, but all we can deduce right now is that Bingo Morihashi probably intended Nero to be Vergil's son. But considering he left Capcom, we have no idea whether or not Capcom is going with that idea. We have to remember that DMC4 was originally very different, it had a different story that gave Dante his own journey and bosses in hell. Even Nero looked very different from what he looks like now, so can we really say for certain that he's still supposed to be Vergil's son? A line in an artbook that was probably originally written by Bingo is not exactly 'evidence'.
I don't think Vergil being his father makes much sense, considering Vergil would never saddle his son with the problem of being 3/4 human, because he thinks power is the ultimate goal. He equates power with being demonic, and if he had a son with a human, that would mean he'd be saddling Nero with the same drama he himself went through as a child: not being able to protect the ones he loves. I also doubt he would just have a child with somebody and then leave them to fend for themselves... to Vergil, that would be a guarantee they'd die from a demonic attack.
Secondly, I think Vergil reveres Sparda too much to dilute the Sparda bloodline like that, and to risk the bloodline dying off completely if demons became strong enough to beat Sparda's descendants.
Third, Vergil doesn't seem to like humans, which makes me wonder why he would want to have a child with one. And if he didn't want to have a child, then how did Nero come into existence? Probably not in the normal, natural way. It's possible the Order of the Sword found some way to create him, or Vergil did in secret (though Sanctus at least appears to have always known Nero is Sparda's ''blood'').
I don't know, there is more symbolism in DMC4 that implies Nero is connected to Sparda, than there is to suggest he is to Vergil. He's got red and blue clothing, his arm is red and blue, his weapons are the Red Queen and the Blue Rose, and Berial says he's just like Sparda was. Nero's story is essentially Sparda's, only reversed: Sparda became human for the sake of living with Eva while Nero ''became'' a demon, came to terms with his demonic side. Nero's original art showed him without Vergil's soul, with his own demon form, which seems to imply he has a surprising amount of power for being 3/4 human. There's something fishy going on. To me, it's almost like Nero was somehow created from Sparda, and it makes me wonder what Vergil was doing in Fortuna. Was he just hoping to get more info on him and what he did, so that he could open the hell gate in DMC3, or was he doing something with Sparda's 'blood'? The guy reveres Sparda, so for all we know he tried to create some kind of clone. Maybe he thought he failed, but somebody went on to create Nero anyway? The story of a prostitute leaving Nero at the orphanage is fishy, anyway, and if Nero has a mother, why wouldn't she be featured at some point? Why wouldn't she even try to find out how he's doing? I think it's more likely he was somehow created, though by whom, we don't know.