Well my best guesses:

1) Bad relay or ground

2) IACV is garbage if you already cleaned the screen. Very common on all F-Series engines for those to shit the bed or you need to bleed the line.

3) Not so sure about this one. There's lots of things that would prevent VTEC engagement. Low oil, bad PCM, crapped O2 sensor, MAF sensor. But those would all trigger CEL's.

Seeing as your car is popping at 4400RPM when you let off, the car is dumping additional fuel for VTEC operation (pooling into the cylinder and you're running rich, hence the backfire).

VTEC solenoid? Sensor? I'll have to think about this for a few.