Sorry to nitpick :D, but the surplice itself traces its origins to the alb, which became smaller and smaller by cutting. Of course, in some non-Roman rites, they wore, or wear, albs instead of surplices. I myself was not used to servers wearing ‘server albs’, though. The first time I saw one, I was thinking, ‘Why are the servers wearing habits?’ due to the ‘hood’ on their albs, which no doubt is inspired by the Amice (which Servers wearing actual albs in other Liturgical Rites also wore, if I’m not mistaken). Until then I assumed that all albs are hoodless. :o
As for the cincture, I think either left or right side is fine.