Yes they have trophies. Since most of the games featured on PS now (probably all of the games actually) are PlayStation 3 games, they all come with the same trophy sets that those games had. I can't say for sure if it is a separate list allowing for you to get the same platinum a second time, but it will most definitely be the same list that the PS3 game had and if the original game had trophies, the PS now version will have trophies too.
