All sounding good. That lines up a bit with his memory-- Gordon only gets a brief cameo in one episode and there's not really any indication of what kind of relationship he may or may not have with Bruce, but Barbara is referred to in promotional materials as "Dick's oldest friend" so I imagine they were back and forth at each other's houses plenty often. I headcanon that he was exposed to her pretty early on, maybe Gordon was investigating the Graysons' murder and he got to know Barbara somewhere in there. But they go to the same school and Barbara's pretty consistently one of the few who can really, really get the better of him. "She's, like, ridiculously good at everything." And he makes a face.

He loves her, really, he just doesn't know how. |D He's kind of confused on that score, because she kisses him on Dec 1 during a game of Spin the Bottle/Seven Minutes in Heaven, and asks him "Why do you think?"

Gymnastics'll be familiar to him, too. Word of God is that Barbara was a gymnast first in YJ continuity, too, so that's probably their major point of connection-- shared hobbies!