As far as our community has tested EPSXe doesn't work well with the Twisted Metal games. Only some versions and certain BIOS in combination give a barely playable experience. We have settings requirements for Duckstation for all the games to prevent that advantage. The PS2 console which is allowed plays all the Playstation 1 games in the series better then any PS1 so Duckstation is totally fine to use with our speed limit requirements.
As for the FanGame I'm not sure if it's uses Music in the series but I could be wrong. Over time the AI use for the game will stop as they have been picking up dev help so hopefully they don't get in trouble.
All the Twisted Metals have speedrunning quirks that make them all different enough to be interesting. The series kinda has been left abandoned so any game is fair game to speedrun.