That actually sounds fairly normal... these engines for whatever reason like to chatter a lot at higher mileages... either that or I seriously need to fix something with my engine. When I pull my valve cover the only thing I really see is a bit of varnish... no sludge or major carbon deposits and no apparent wear on the cam lobes or lifters.
Whats is the best way to find these problem?
Best way? Pull off the manifold and replace the gasket. Another way to do it that I hesitate to try is to spray carb cleaner around the various vaccuum hose connections and throttle/intake gasket surfaces while the engine is running. If you hear the engine rev you know you've found a vaccuum/intake leak. I hesitate to suggest it simply because of the possibility of fire and I don't know if it could cause damage with these engines... someone will have to clarify that.
What should i do about the cold air intake if its the case?
Nothing... that's part of why people install these systems in the first place.
Isnt the car has a stock short ram intake?
No.
Notice the rest of the air cleaner assembly still remaining in the engine bay? It continues all the way down underneath the battery and has an intake tube at the front of the engine bay behind the headlight. That's not a short-ram intake.
How can i flush the motor?
Marvel Mystery Oil or AutoRX. I've found MMO to work somewhat better than AutoRX. That, and it's a hell of a lot cheaper.
That intake will likely have even more of a whooshing sound. In all seriousness, though, I would just stick with the stock airbox/aircleaner. You get better fuel economy and better power at the lower end of the power range. A whole 5HP at 5000 RPM's is hardly worth the headache. Although, it does look really cool!
You probably noticed that i am using an custom air filter, and to prevent the check engine to light up, i took the sensor and pluged it back without a filter, does it mater?
Yes. Without that MAF in the correct place, your engine computer has no idea how much air is actually entering the engine. The fact that it's running at all means that it's probably running in open-loop mode but the fact that the CEL hasn't popped up is interesting to me.
I just took a closer look at your videos and I see three issues.
1) Your MAF isn't hooked up to anything. Your engine will run like crap (amazed it's running at all) like that.
2) That's why you're getting a lot of that hissing sound -- the stock air hose isn't designed to for that type of filter and you're probably getting some air leakage around the air filter base in addition to the normal hissing/whoosing noise those types of filters create.
3) If you want to install a CAI/Short ram intake, you need to use the supplied tubes for it. Sticking on a filter like that is not the way to achieve what I think you're trying to do. And, more than likely, it's what's causing that loud hissing/whooshing sound. The tubes supplied with the K&N and Weapon-R kits like the one you linked to are designed to include the MAF in the air stream also.
Also, my car has 2 sensor right? 1 before the catalytic and 1 after?
Depends on which sensors you're talking about. It sounds like you're talking about your oxygen (O2) sensors... so yes, there are two. One on the downpipe right after the exhaust manifold and one on the exhuast pipe between the cat and the resonator. That, of course, doesn't include the dozen or so other sensors that are part of these cars.
