Lots of problems, think it might be a simple answer.

I recently bought a 2001 Honda Prelude SH. I have had it for about a week and have noticed several problems. First of all, I am getting about 14 and a half miles per gallon. The rev limiter kicks in at about 6500 rpm. The car has a rough idle at very low speed. The exaust backfires a bit. The VTEC doesnt seem to be kicking on (my friend thought I had the H23 engine when he drove it because he couldnt feel the vtec kicking in, but the block says H22A on it). And finally, the car has died 3 times for apparently no reason. I think 3 of these problems have to do with having a rather large cold air intake and a rather small muffler, getting too much air in and not letting enough out.I believe that would account for the low idle and backfiring and maybe the dying. What I think might have happened with the other problems is that the person who owned it before me had some other aftermarket mods on the car (I cant spot anything else under the hood) and took them off when he sold the car, but left the settings for the sensors(dont know what that is called, sensor mapping?) Modified for what he originally had on the car. I know that disconnecting the battery for 5 minutes is supposed to reset the computer so I dont know if there was a chip on the car or not. I was wondering if there was a chip on the car, would it account for these problems, or am I looking at more serious problems or maybe just needing to change a few sensors?