Here is what we did with an old Bowser turntable. The turntable came with a large plywood disk below the floor of the pit. The disk is attached to the bridge above the pit by a central stud. To turn the disk we mounted a motor with a rubber wheel onto a board with a door hinge on one end. Several rubber bands provide adequate tension to give the rubber wheel traction and give flexibility for any unevenness in the plywood disk. The motor is powered by the transformer hiding nearby (from Lionel's RailBlazer) This particular transformer has AC and DC outputs. In DC, clockwise is one direction and counterclockwise is the other. Strait up is 0 volts. The transformer hums slightly when any power is going through it, providing feedback to the operator's hand and preventing us from burning out the motor by leaving it under load (or use an on/off switch).
Power comes to the track in two ways. The ground comes through the track and wheels in the pit. The hot wire is strapped to the stud that connects the disk and the bridge. You can see the wire dropping down from the stud in the two lower photos. To avoid the problem of the wire getting all twisted up we used an old meter lead with a coupling. Every once in a while the meter lead is uncoupled and unwound. Also we developed the habit of operating the table in both directions, this is now an unconscious habit.
I hope this helps answer your third question.
Nathan