Engine stumble????

I got the sr20 running pretty good now put about 80 miles on it today having fun. The problem I have now is that 1 it doesn't idle quite right if I rev it and then let off it stumbles after a grand and dies, BUT if I let the gas down slowly to about a grand it dips down then back up then back down and does this a couple times then levels out and idles around 800rpm like it should what could be causing that? ALSO when driving down the road (only noticed so far around 2k-2.5k rpm) the car stumbles and acts like it is dieing, but If I give it some gas it responds to that and runs fine it only has problems when trying to just cruse at low speeds (45 or less) What could be causing this? MAF? Also the injector harness has a ground coming off of it correct?

check your AIV or clean your MAFS and see if it helps..

clean your fuel injectors

or can it be the fuel pump?

my sr has the same problem w/ stumbling in idle it normally just happens when i come to a quick stop