The Korean

2005 RX8 GT 6MT
Car: ~435XX miles
New Motor: ~6XX miles
Rebuilt Trans: ~6XX miles
Clutch: Original clutch
Mods: Intake, cat delete race pipe, catback exhaust

So I haven’t taken the car back to the dealer yet, but I'm already having major problems with the new motor... could be the clutch, but I'm pretty sure it's the motor.
When it's cold and you start the car it either dies right away or it stays running til you put it in gear and start tot drive... then it dies. Now I know you have to warm the car up before you drive it, but do I have to warm it up every single time the car itself is cold? I was under the impression that it only needs to be done once in the morning. I started noticing the problem around Sunday night. Actually it wasn't bad til then.
Sunday night... car hadn't been driven for a few hours and went to go get food. Put it in 1st and drove 100 yards perfectly fine. Then after that it started to stutter like it wanted to die... and got "bouncy" like you weren't giving it enough gas. Pulled over, let the car warm up a little and then it drove semi fine.
Monday morning... I needed to move the car at work. Again it hadn't been driven for about 3 hours and moved it. Put it in gear and started driving... it died. Started it back up and let it warm up. Fine after that.
Tuesday (today) morning... Ready to go home in the morning started the car to let it warm up and it died instantly. It revved to about 3/4XXX and instantly died without touching it.
Things I've noticed over the past couple days. In the lower rpms, it feels like it stutters and isn't getting enough fuel or air or something. It's mainly between 25XX and 5XXX rpms. It almost feels like it wants to get up and go, but can't. Also, my wideband gauge reads "---" when I'm about half way down on the gas. It will sometimes read in the 17/18 range, but mainly it reads "---" til you get floor it then it AFR's drop to around 12.X. Last but not least the check engine light blinks more than normal. I have a cat delete race pipe on so it's on all the time, but it never blinked this much when I had the old motor in. It's blinking before the red line mark... like around the 4500/6 area. One thing to note... when you're driving it like an every day driver it has the problem/hesitation... when you floor it it does perfectly fine.
Anyone have any idea?