Downed Power Line Scenarios
In the case where you hit a power line with your car, is it possible if you
  a) touch the frame of the car [(i) either one or (ii) both hands] and your body has no contact with the ground, you will not be electrocuted.


It is current through the body that kills. The levels are quite low and we typically set RCD/GFCI devices to 30 mA as a safe limit.

To get current to flow through the body a voltage (potential) difference is required between two points of the body. Since the car's chassis is steel or aluminium all points on the car's chassis will be at the same potential so there is little risk.


  Similarly, if you b) open the car door and have one foot on the ground and the other foot still remaining in the car. (keeping in mind that that the body is not in contact with the frame of the car)


You are relying on the insulation of the carpet and your shoes. This might be OK for domestic voltages but not for distribution voltages.


  I may have misunderstood something, but is the reason that you do not get electrocuted due to the negligible potential difference for scenario a) with both hands and that one hand touching the frame will result in the same reasoning for scenario b) where you are not completing the circuit that you won't get electrocuted?


You are missing the capacitative current.



Figure 1. Electric shock through body to ground capacitance. Source: All About Circuits.

I can't find a good illustration but if you imagine that's a capacitor between the guys body and the ground then with AC voltage an AC current will flow through the body capacitance to ground. This effect is used safely in neon screw-driver type phase-testers by including a high value resistor in the circuit. Without that there is danger of electrocution.

For power distribution systems at higher voltages it is common to fit ground fault detection relays which, if a ground fault is detected, connect that phase to ground to reduce the risk to anyone coming in contact with the wire.