Why should you stay in the car during thunderstorms?
Yes, if it is not a plastic covered car it is an effective Faraday cage.
If the tires are such that the car is insulated electrically, if it is hit it will take some time to discharge to the ground, but still the passengers would be safer than standing next to it outside. I have learned that modern tires are particularly constructed so that the static charge generated by the friction on the road is discharged so that would also help. ( in olden times they used to have chains trailing from the trucks in order to discharge the static. Recently I saw a car with a discharger too, trailing on the road!).
lightning is essentially just an huge electric arc from the clouds to the ground, correct?
Wrong, the current actually may start from the ground. That is the rational of the lightning rods, to create a path for a current to be generated by the potential difference to the cloud and to meet the current from the clouds in a prefered location instead of a random one. It is not wise to stand next to a rod, read in the link the amount of power dissipated by a bolt.
The average peak power output of a single lightning stroke is about one trillion watts — one "terawatt" ($10^{12}$ W ), and the stroke lasts for about 30 millionths of a second — 30 "microseconds".[18]
And it is not wise to stand, because you may also give rise to leaders that will meet the lightning path. If in the open it is best you fall on the ground as much sheltered as possible.
A colleague once was about 20 meters from a lightning bolt, and he was so shocked by the sound and fury, it took him a week to come down to normal.
In answer to your second question: "Now going with my b) reasoning, wouldn't you be just as safe standing next to a giant conductive pole (i.e. a lightning rod)? Wouldn't the lightning just go through the lightning rod and you'd be 100% safe?" No. A lightning strike can carry a high current, up to 200 kiloamps has been recorded. Not only can the current be high, but the rate of change in this current is high as well. That means the induced magnetic field around the pole and the path of the lightning can be quite high. This can induce high voltages in the vicinity of the strike. In fact many people who are reported to have been "hit" by lightning, have not taken a direct hit, but suffer from induced currents.
You are correct about the widely misunderstood thing about rubber tires. A spark that has enough voltage to travel thousands of feet, will not be stopped by the few inch gap between the conductive part of the car and the ground.
Be careful about your definition of giant conductive pole (ie be exact in you description).
Some people may consider trees as a conductive pole. The danger here is not only from electrical discharge but from exploding tree (due to sap boiling in an inclosed space).