Re: I wonder if the detected planets so far have any pattern to their orbital planes relative to the galactic plane?
There is no "up and down" or "back and forth" in space, Only tilted toward or away from us. I.e., the plane of the other solar system is either face-on, or edge-on to us, or some intermediate point in between. A rotation of the orbital plane on the celestial sphere (about the line-of sight axis) is physically and geometrically meaningless. The observer could cancel it out by just tilting his head.
Yeah, it gave me fits too, when I was a student