The reason you need to "tune" when you change components is to compensate for the changes. For a CAI, the only time you need to change anything is if the MAF sensor is moved or the MAF housing is increased or decreased in size. The MAF sensor measures the amount of air passing by, but it only samples the air, and the PCM uses that reading to determine the amount of air going into the engine based on the area of the MAF housing. If you increase the MAF housing size, more air flows, but the computer would "see" less air, so it would "lean" the fuel mixture. The tune needs to be modified to compensate for the different sized housing so that you can get back to the proper AF ratio. If the MAF sensor is even moved, and sits in a different angle than before, it will be off a little, and the tune needs to compensate for it.
If you tune for performance, you are adjusting the two parameters that affect power: AF ratio or spark timing. If you go a little leaner, you make more power (within reason). However, as you go lean, you make more heat. Heat can cause pre-detonation of the AF mixture which can damage the engine. Also, the leaner the mixture, the easier it burns, so both factors tend to lead to pre-detonation. Advancing your spark timing leads to more horsepower at higher RPMs (typically less torque at lower RPMs too), but just like leaning out your mixture, if you advance the timing too far, you run the risk of detonating your AF mixture too early.
The reason you would run higher octane fuel is because the higher the octane rating, the harder the fuel is to burn. This allows for leaner fuel mixtures or more advanced spark timing. You have to adjust the tune for more spark or leaner AF ratio if you want to take advantage of higher octane fuel, and once you do that, you can't start running lower octane fuel again unless you want to risk causing damage to your engine. Newer cars (like the 2011 mustang) can detect when you have higher octane fuel and automatically give you more timing, giving you more power. However, even if you don't have a tune for higher octane, there is nothing wrong with running higher octane fuel with a lower octane tune. It's the other way around that can be bad for your motor because of the risk of pre-detonation.
When running boost, the AF ratio is very important. At WOT, if you are running 14:1 Air to fuel, with even a small amount of boost (or high compression in a naturally aspirated engine), you can start to melt aluminum in a very short amount of time. The higher compression combined with lean fuel creates some extreme heat, and not only is detonation pretty much a guarantee, the pistons, block, and heads can be damaged just from the heat alone. Boosted engines run in the 10.5-11.5 range at WOT, depending on fuel, spark timing, and intake air temperature.
It all comes down to safety of the engine, with intake air temp, AF ratio, fuel octane rating, and spark advance being the deciding factors on which parameters you can push and which ones you can't.
The engines are fairly safe from pre-detonation with the knock sensors constantly "listening" for a ping. If pre-detonation is detected, up to 25 degrees of timing can be pulled from the tune automatically. This will drop power drastically, but allow the engine to run under abnormal conditions without any threat of damage. However, a major change to the engine without compensating for it in the tune will lead to all sorts of problems.
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