OK, here's some answers in a slightly random order.
Overdrive: this is, in effect, a separate 'gearbox' that sits behind the main, 4-speed gearbox. It's operated by a solenoid, that switches the unit between two ratios (when switched off, it drives through a central shaft and makes no change to the gear ratio, when switched on, rotation is passed through a system of planet and sun gears). This sort of shows you the basics:
overdrive has the advantage of not requiring the clutch to be depressed when you select/deselect it. It has the disadvantage of sapping power.
As to the Spitfire, the bonnet is by far the most expensive bit on the car. If it's junk, it might be worth looking for a different car. A solid chassis is important, but it's not actually that difficult to repair: everything unbolts from it, like Meccano. The chassis outriggers are particularly prone to rotting, but again are fairly cheap and easy to replace.
It's very hard to put a value on the car without seeing it, or at least pictures of it. Is it MOT'd? With such a high mileage, rotten panels and no MOT, it probably isn't worth more than a couple of hundred quid. You might also be better off buying a better example in the first place: it's probably cheaper than restoring a bad car.
You will have to pay car tax in this vehicle. Gordon Brown froze the 'classic car' status to apply to cars registered before the end of 1972.