Without hondata flashpro or ktuner (ability to tune the ecu), you'll probably not see any gains. An intake will make the engine sound better, but you'll not really see any gains. The car would need tuned.
You take it to a dyno shop, or have the car e-tuned through email with flashpro or ktuner. If you opt for etuning, you email the tuner data logs and they adjust fuel/timing, etc. It's not something you plug in and it just works.
k&n filter tends to let more air through versus a stock filter. You probably won't really see any gains with it, but you won't have to keep replacing your stock paper filter. It'll pay for itself over time.
As a fellow R18 owner, I would say skip it. It won't do much for you but cost you money. If you want it just for something to do and the bling factor then get it. You won't see much in the way of HP gains though. The car will be a little louder. I second webby in getting a K&N drop in filter if you want to do anything. The R18 does not respond to mods the way the K series engines do. Everything is designed for fuel economy and the car will fight you at every point in trying to gain power. Adding "lightness" is one of the best ways to go on these cars. Not to discourage you but just to give you honest feedback.
It's your car though and you should do what you want! Id suggest spending the money on wheels/brakes/suspension first. There is a lot you can do to make the car very very fun to drive.
Thanks for all the input guys. Yeah I'm definitely not putting money into the car as far as performance parts go. I'm going to be spending a lot on cosmetic things. I just wanted a little more aggressive sound with the sri but if it's going to be harmful to my car then I can do without.
It won't harm anything. It just won't give you massive HP gains. If you want to do it for sound and looks, go for it! Just be informed. It's possible you will get better MPG but heatsoak will be worse especially in the summers and when sitting in traffic.