Possible fuel problems

Hello, I have the vehicle listed above, GTST with a rb25det engine. I currently am having a problem where the car will cut out (as if fuel stops delivery ) when full throttle, however if I build up to the boost and accelerate slowly no issues at all. Also, the car sometimes idles very low and almost stalls to the point where the battery indicator on the cluster instrument will light up for a split-second. Last thing is the car needs some throttle when starting up otherwise it will start and shut off instantly.
it seems as if there is not enough fuel supply or perhaps an injector problem? This is just my guess. Will appreciate feedback.