We don't know if this woman is good or evil. I don't see anything creepy about her behavior, she just holds her hands in a sort of praying way - as if she noticed it was Vergil, and she felt humbled and/or excited.
The color red is connected mostly to people of low social standing. She looks like any other pious civilian. Considering she came from the direction of the opera house, she might work for the Order. Vergil didn't recognize her, and she didn't approach him, so I would assume they have no relationship.
As for Vergil having a child with a human woman... I'm skeptical. Vergil sees humans as weak, he probably thinks Eva was weak for not being able to defend herself and losing her life, leading to Dante and Vergil's probably cr@ppy lives. It's the opposite of Dante's hate for his father: Dante thought Sparda should've made preparations for a possible demon attack, or should've found some way to retain some demonic power, but he didn't and Eva died because of it. That explains why Dante claims ''I don't have a father''. So Vergil's disdain for humans doesn't necessarily have to do with that woman, it's probably related to Eva's death.
Since V wants to emulate Sparda, maybe in DMC3 he said ''without power you cannot protect anyone'' because he wanted to protect his kid (Nero). Maybe Nero's mother died because he couldn't protect her... so Vergil left Nero at the orphanage to protect him from demons. In other words, Vergil was trying to keep Nero secret, so that he wouldn't be targeted by demons like Eva and the twins were. It also explains why Dante still doesn't have a spouse: because demons are drawn to him and he doesn't want to put his family in danger.
However, it's also possible that the reason why people thought Nero was born of a prostitute was because he wasn't conceived naturally (experiment).
And yet, I still like to think it's all connected to Sparda. DMC4 has many Sparda-related themes, so maybe what happens in DMC4 SE will be connected to Sparda too. For all we know, Sparda's DNA was on one of the artifacts in Fortuna, and Vergil used it. Who knows.