Nuada's fighting style is mostly based on speed and agility, doing all kinds of elaborate maneuvers to land hits on his opponent without being hit back. And he shares a magical link with his twin sister that means that everything that physically happens to him also happens to her and vice/versa. It stands to reason that he developed his fighting style in order to keep his sister from getting hurt along with him, supported by the first fight scene where he gets hit in the face and then turns to Nuala, clearly horrified as they both start bleeding.
Hellboy's Kind Hearted Cat Lover traits make sense due to his hellish origins. Cats are believed to be the gatekeepers of the underworld.
It's entirely possible Hellboy didn't prevent the apocalypse, he just assured that it would happen when it was meant to. He barely aged a year after over 300 years in hell, and he's in his 60s to 80s, so the apocalypse likely isn't meant to happen for millenia. This also implies he COULD have been the anti-christ if he hadn't been summoned to earth.