We have towed everything from a micro 2 door to a full sized (SWB) van (pulled the driveshaft) with our EZE-Tow.
The dolly will have no issue with the Murano (Edmunds says it weighs between 3500-4200lb as optioned). I would call Acme to see if they have any first hand experience with the Murano. Richard Brown (the owner) has been very helpful when I have had a question...and they are a sponsor here if you want to send a private msg.
You are right that the steering must be unlocked so the car's steering can pivot - just like for flat towing. If the accessory position will work to unlock the steering, then you are good to go...but be sure the computer will not shut off the juice after a pre-set time.
If you are worried about the battery draining while driving, a small dashboard solar panel plugged into the cigarette lighter/power port will top-off the battery while driving in daylight. At night, you might want to switch on the car's parking lights to illuminate the rear end corners (not required by law everywhere, but a good idea), so that is add'l battery drain. If you intend to drive for long periods at night, you might consider adding a circuit between the RV and the car to keep the Car's battery topped-off.
A power lead between the RV and the car can be a simple fused 2 wire (positive and ground) with quick connect.
You might ask your dealer to disable the steering lock to ensure it never inadvertently engages. It is a simple solenoid driven bolt in the steering...similar to the power door locks. They would just remove power to it while disengaged and it will stay unlocked. Steering locks are becoming a thing of the past because thieves can easily overcome the lock...and are not even standard on many new cars.