They definitely could have done better. I liked when he was like dudes I am out of any answers ok. I can hardly blame him, he'd dealt with so many people letting him down at that point. LOL. Like sometimes even the Purely Good Nice people need to let loose and hate everything.
Billy is actually a villain named Jigsaw. He was a criminal underworld hitman guy, he didn't have the background with Castle at all. Their background was that Billy was tasked on killing everyone that Frank knew after the botched assassination, and then Frank was like fuck you and scarred his face horribly. From then on his major goal was just to fuck with Frank and make him miserable and eventually kill him, he wanted to make him hurt a lot first. The film actually showed the more truthful Billy, the 2008 one. Just a really ambitious mob hitman who blamed Frank for messing up his life and went on a vendetta.