To answer the questons;
(1) Yes, a car trans will work just fine. In fact, the one in my '55 3200 is from a '55 Station Wagon.
(2) Definetly the cable if you can get it. You'll also want that bracket ans switch that's on the carb if you don't get the engine. That switch is the kickdown, and is difficult and expensive to find in the aftermarket, as it isn't being reproduced. The harness not so much, as the Truck specific version is readily available new. You'll also want to get the relay, if it's present on the car.
(3) Yes, overdrive was an option.