(1) To address your first question: you have to treat the cloud and the earth below it as forming as a capacitor. There's a good popular description of this at http://micro.magnet.fsu.edu/electromag/java/lightning/. A capacitor is described by it's capacitance, and this is related to the voltage and charge by:
$$C = \frac{Q}{V}$$
where $Q$ is the electric charge and $V$ is the voltage difference across the capacitor. You can approximate the cloud and earth as a parallel plate capacitor, and the capacitance is given by:
$$C = \frac{\epsilon A}{d}$$
where $A$ is the area of the cloud base, $d$ is the spacing between the cloud base and the earth, and $\epsilon$ is the permittivity of air ($8.854 \times 10^{-12}C^2N^{-1}m^{-2}$). Combining the two equations and a quick rearrangement gives:
$$V = \frac{Qd}{\epsilon A}$$
This is obviously a gross simplification, but should give you a rough idea of the potential difference.
(2) As to your second question: as you say, positive lightning requires a higher voltage to get it started. Looking at the equation for the voltage, assuming the cloud stays the same the only way the voltage can be higher is if the charge is higher. Current is defined as charge per unit time, and if the duration of the lightening strike is roughly constant a positive lightning bolt has to transfer more charge in the same time and therefore has a higher current.
The lightning rod is based on two principles theorized by Benjamin Franklin. Lightning dissipation theory, and lightning diversion theory.
Lightning Dissipation Theory
This theory says that if you point a pointy metal object toward a polarized cloud, the metal object will be able to bleed off some of the energy from the cloud. Thus preventing a lightning strike.
This theory can actually be demonstrated, using a Van de Graaff generator and a nail. This YouTube video demonstrates the theory.
While this theory holds up on the small scale, it's been shown not to be effective at dissipating the large amount of energy built up in a storm. Fortunately, the design of the dissipation device (lightning rod) is also a great diversion device.
Lightning Diversion Theory
The lightning diversion theory says that if you provide a preferable path for the energy to travel along, there's a high probability the energy will follow that path.
Lightning rods are designed to be the highest objects around. This puts them closer to the polarized cloud, and reduces the distance the lightning must travel through the air. They are also made from conductive materials, and are connected to the earth through highly conductive materials. This provides a low resistance path to ground, making it a preferable path for lightning to follow.
While both theories hold up in the laboratory, only diversion theory seems to offer a viable lightning protection system.
Best Answer
Lightning also has a massive electromagnetic field that is created during a discharge. This field is so strong and changes so fast that it induces current into anything metal. This is like a big electromagnetic pulse and it flows everywhere. If strong enough it will fry anything with a PN junction (diodes and transistors). In fact you don't need to be hit by lightning for it to fry your electronics. A nearby strike can create a big enough pulse to cause damage. Grounding isn't really so much an issue. Most cars have poor grounds because they sit on top of air-filled tires.
However your car is surrounded by a lot of metal. This metal can act as a shield from both the electromagnetic fields and the flow of the discharge current. This factor can prevent both damage to you and your electronics. This also makes the damage due to lightning very random.
In general lightning goes where it wants.
When we are talking about strong charge densities like found prior to a lightning strike, the "ground" isn't ground. In simple terms it takes an active role because the electric field between it and the ground attracts opposite charges. Big clouds filled with charge moving over the ground pulls positive charges along with it. You can physically measure thousands of volts of difference between spots on the ground due to the movement of overhead charges.
You have to imagine the entire system to get an idea of what is going on with the charge.
So on the ground around your car you have a lot of positive charges that will try to get pulled up to the metal on your car and then pulled up towards the roof. The amount of charge your car builds up depends on how well the charge can conduct from the ground through tires/water/mud to the body.
Your confusion about a "negative chassis" is only in relation to your 12V battery. Your "negative" on the 12V battery is only relative to the "positive" on your 12V battery. If the ground is at a potential of 10,000V, then your positive is at 10,012V.