Yes you sure can drive in the pasture. I don't have a ring, so I drive in the pasture or the fields. You can do anything in the pasture you can do in the ring, practice circles around trees, practice straight lines, backing, transitions etc.
It will be good for him to be distracted, there will be lots of distractions at the show.
Keep contact with the bit, about one pound in each rein, this will help him to pay attention to you and nothing else. Failing to keep contact is probably the biggest mistake beginner drivers make. Contact gives the horse a sense of security, knowing you are there telling him what to do.
To practice turning, do turns, do sweeping turns now, you can do tighter turns when he gets good at loose turns. You can practice circles, serpintines, transitions, both up and down. I would hold off practicing backing, I consider backing an advanced move in driving. I usually back once a drive and that is it.
I think for your first show you should concentrate on, consistency in your gates and smooth transitions, contact with your horse will help with both of these.