First off, you're wasting your money on a cold air intake. Even in those rare occasions when they do increase HP, it's only in the 5,000+ RPM range. Find the cold air intake model you're thinking about and then look up the power ratio chart to prove it to yourself. Follow the increased HP curve and match it to RPM. You'll be shocked at how little boost you get at RPMS lower than 4,000. How often do you drive in that range? Plus, don't confuse more HP with better gas mileage--the two are mutually exclusive. The entire theory behind a cold air intake is that cold air is more dense so you can pack more molecules into the cylinder. But since the MAF knows the density of the air, so it adds more fuel to get the perfect mixture. More fuel equals fewer miles per gallon.
One more thing about cold air intakes. The part the manufacturers don't tell you is that although cold air is less dense, it is also COLDER. Since raw gas doesn't burn (it has to be vaporized first) car makers intentionally use under hood (hot) air to assist in fuel vaporization. Put in a cold air intake and you forfeit all the advantages of vaporization. What's that mean? Poorer performance at low RPMS in cold weather.
Second, most "cost air" intakes are really nothing more that vroom-makers. If the air filter installs under the hood, that's NOT a cold air intake. To qualify, a cold air intake must take in OUTSIDE air from in front of the radiator, the wheel well, or under the front bumper.
Next, there is absolutely NO difference in power between 87 and 93 octane. None. Nadda. They both provide the exact same number of BTU's. The octane in 93 just increases the flash point. That's all it does. A higher flash point prevents pre-ignition in a high compression engine. Put 93 in an engine that specs 87 and at best you're just throwing money down the drain. At worst, you'll experience hard starting in cold weather (since you've no increased the flash point of the gas).
Read this about 87 versus 93 octane
87 versus 93 octane
Next, be very careful when you mess with the exhaust. These engines are designed to require a certain amount of exhaust backpressure. If you reduce backpressure, you can actually DECREASE power. It all has to do with valve overlap--that short period of time when the exhaust valve is closing but not yet closed, and the intake valve is opening. Reduce backpressure at that point and the exhaust that's rushing out of the cylinder will actually sweep some of the new air fuel mixture out with it.
Finally, gutting the cats is illegal--like $10,000 fine illegal. I'm reasonably sure (but will have to check my Alldata) to see if there's a post cat O2 sensor on this vehicle. Gut the cat and you'll be throwing trouble codes and the PCM will pretty much go nuts.
Want better gas mileage? But a different vehicle.