Personally, I avoid using Bernoulli to describe lift or downforce. It's complicated when it's not a closed system and there is turbulence as in the real world. Newton always applies though. The amount of force perpendicular to the direction of travel (lift or downforce) will be equal to the net sum of all the affected molecules of air times their individual rates of accleration as an object travels through the air. Unlike an aircraft, F1 cars have a lot of drag, not much better than their lift. For 2005 and earlier, when they ran 3 liter V10 engines at 900+ hp, top speed was limited between 185mph to 235 mph based on wing settings. If you look at a video of a F1 race car in the rain, you see a huge rooster tail caused by the upwards acceleration of air by the wings on the car.
In F1, underbody tunneling is not allowed (it is allowed in the USA similar Indy Race League and Champ Car racing series). Instead a flat skid board that wears based on contact is used to check for a F1 car being set too low.
F1 uses a racing oriented traction control system (except for the initial launch and when exiting pits). Rather than eliminate tire spin completely, some tire spin is allowed, usually around 8% or so. The rules in F1 require that this be handed by the ECU engine management, and not by individual wheel braking (wheel braking is referred to as stability control in the racing world). The F1 ECU's cut off fuel to cylinders in a pattern, depending on how much power is to be reduced, although power cut of is limited so a driver can't just peg the throttle, but the driver is able to push the throttle such that the traction control is enable, which mostly helps at low speeds.
For safety reasons, F1 and other high downforce racing cars are setup so that at high speeds, the downforce creates more relative rear end grip than front end grip, creating a slight understeer response. This is to prevent snap oversteer (cars spinning) at high speeds. At low speeds, the cars typically are setup with a bit of oversteer since it's quicker, and at low speeds there's less danger, and traction control will help reduce excessive throttle induced oversteer.
F1 cars do not have a full frame. The monoque carbon fiber body itself is the main frame, and there is a driver cage, front sub-frame, and rear sub-frame on the car. Heat sheilding is used at the rear to prevent the carbon fiber from getting overheated by the engine and turbocharger.
Back to the downforce, the amount of downforce and drag versus speed is adjusted based on the requirments of a particular track. On average there's 1 g of downforce at around 115mph. With a high downforce setting top speed on a straight can be reduced from potential 235mph down to about 185mph. In high speed turns, about 4 g's of lateral force can be generated, but this consumes enough energy, that top speed is futher reduced to about 160mph or so with the high downforce setting. If I remember correctly, the cars produce about 1g of drag around 155mph, which translates into 5g's or more of braking (1g aerodynamic, 4g's from the tires) at speeds at or above 155mph.
The tires produce about 1.5g's of force in a non-downforce situation. The increase in grip versus downforce isn't linear though it takes more than (4 / 1.5) 2.6g's of downforce to increase grip enough to pull 4 gs in a turn.
I'm not sure about F1 cars, but the heavier Champ Cars use 14 layers of carbon fiber cloth (and a lot of resin) to produce the monoque body. A team sprays a mold with mold release, then places the 14 layers and resin into the mold, then places the entire structure in a non-stick pink plastic bag, which is then put in a heated chamber and the bag is evacuated to force the carbon fiber cloth tightly into the mold. F1 cars may use few layers or lighter cloth than Champ Cars as F1 cars are about 200lbs lighter (around 1200 lbs versus 1500lbs). There are two main body pieces, the top and the bottom part.
There's a DVD named "Super Speedway" about Champ Cars predecessor, called CART, that includes a video of the process in creating a Champ Car body.
