1: Yes, just ctrl+drag over the objects you want to see the barycenter for, then click on one of the info tabs that appears on the side of the view, this will bring up the multiple bodies window and there's an option to show the barycenter there.
2: you can start premade simulations paused, and i think doing so will make your own saved simulations start paused, though I'm not sure how reliable this is.
3: As far as I've seen, no, you can't reset the time or use another counting mechanism.