The problem with procedures like those outlined above is that they make the assumption that a) you have
common sense and b) you know what you're doing. This is, in my experience at least, sadly not always true. While I do not dispute the
effectiveness of any of the above, I would like to offer a few
safety points from the POV of one who has seen friends screw up while
racifying cars, even when they
did have common sense and
did know what they were doing. So by all means, if speed is your thing, PLAY! Just please exercise a bit of safety.
Lower-diameter tires will indeed give you more torque. They will also make the car less able to handle the sorts of bumps that everyday driving will throw at you - road joints, potholes, ramps, curbs, etc. Hitting any of these at any speed will be more likely to 'flatten' the tire against the wheel; this can cause unexpected flat tires (from abuse that any normal tire could withstand), especially if the thin tires in question are 'bargain' versions. Performance tires of this type designed for use on rough but real tracks are typically either solid or contain a high fiber count, both of which make them pricier. Also note that 'performance' tires will typically have more surface in contact with the road (for increased traction). This means that in wet conditions they will lose that traction to hydroplaning much, much more quickly.
Nitrous Oxide, while itself not terribly hzardous, is designed to do things to your engine that the designers didn't want to happen. This is especially true in econobox 4-cylinders, whose engines were designed for efficiency and high RPMs. Modern 4-cylinder engines ride much closer to their physical limits than larger, less efficient mills. As a result, it is much easier to push them over that limit using what may seem like very small amounts of boost (nitrous or air). Start very, very low, and remember, each time you use a nitrous system, you put extreme stress on valves, piston rings, and in fact most of the moving metal in your engine. If the engine can't put out that much torque normally, remember, the moving bits probably aren't rated to handle it either.
Weight reduction is typically quite safe as long as you're not removing structural bits or car systems. ;-) Remember that modern cars use monocoque designs, and don't have frames; some body parts themselves provide structural strength.
Finally, ram air induction. Yes, cold air directly into the intake will boost your power a tad; however, remember, air filters are there for a reason! Bypassing them will allow grit, dust, insects, what-have you and the like into your air system, and there is a reason that racers like their air to be clean-room grade. With an engine already at very fine tolerances, every particle is destructive. The mailbox solution would probably cause a slightly noticeable boost in power - but so would removing the air filters. Both options will likely increase your chance of cylinder damage to extremely high levels.
All this leads me to my final recommendation: use common sense. Remember: the designers of your automobile didn't just design its engine to put out the (maybe currently unacceptable)amount of power that it does. They also designed its brakes to be able to handle that amount of power and speed; they designed its steering to be stable at those lower speeds; they designed its transmission to handle those power ranges. Overengineering, in consumer auto design, means lowering profit margins - remember that. Modifying your car, if you're going to do it for speed, DOES NOT STOP WITH THE ENGINE (and, realistically, shouldn't start with it either!) Most modern autos are capable of more speed than they can safely handle without tweaks - adding nitro and other riceboy gadgets just widens the gap between 'able' and 'safe.'
First, make sure you can drive your car at these speeds. Take a racing course. In the U.S. (with which I personally am familiar; I won't speak for the rest of the world) there are any number of reputable racing schools designed to teach you how to handle automobiles at speeds higher than you are used to. This is not something you 'learn by doing' with no instruction, unless you have a death wish.
Second, while you plan your assault on your four-banger, practice up your wrenching skills by upgrading some other critical stuff. Install high-performance brake pads. Check your rotors; consider putting in high-performance ones that keep cool better and/or perform better when hot. Triple-check your steering. Are those bushings a little worn? Maybe you should replace 'em. How's your power steering/brake belt? A high-perf one will only set you back a few bucks. Check for hydraulic fluid leaks and pressure; higher engine speeds may mean higher pressures in those systems.
Safety doesn't stop under the hood. How are your seatbelts and airbags? If you're not sure, have them checked. If you're going to do this semi-regularly or more often, please, think about investing in a safety harness! That one mod alone can do more to save your life than anything else. Check with the authorities; some places, it's illegal to drive cars with race-prep gear (even just the safety stuff) on the street, under the wonderfully bureaucratic logic that if you have it, you must intend to use it, so you're guilty. Some things are good to have no matter what - a fire extinguisher, for example! Those are legal, and besides your life they can save you oodles of money and angst if a fuel line breaks or an electrical fire breaks out by preventing your hard-tweaked baby from burning itself down to ash. One final tool I've had to use: a safety glass hammer. It's much more difficult to get trapped in a car if you can pop whatever window you're looking at quickly and safely.
Finally, never road-test alone. Don't carry passengers, but be sure there are others nearby watching you who can perform the most vital lifesaving maneuver - calling 911 - if required, as well as warn you of obstacles, problems on the exterior of your car, and the like. Again, most race tracks will offer 'speed days' where you can bring your modified car and test it on a closed safe surface, with professional emergency response folk around. You'll have to sign ridiculous waivers, but so what? It's your choice. ;_)
In any case, yes, by all means, play with your car. Cars used to be meant to be worked on, and any time you spend working on your car will likely make you better able to grasp its limitations and abilities, if you pay attention. Plus, the mundane stuff can save you money if done yourself!
Have safe fun!