If you are hearing marked variation in fuel pump(s) noise at idle (is more of a whining/humming/buzzing to me), and there seems to be a correlation w/the lumpiness, fuel pump(s) and/or wiring/relay would be increasing suspects. But seems you're also getting different cold vs hot behavior
Along w/checking fuel pressures (control pres, warm control pres, residual), ck fuel pump output volume (all should be in Haynes).
When fuel pumps start to fail, they go pretty quickly - within hours IME (they've either been running weakish for a while - unnoticed - or have been subject to recent contamination of some sort). You'll get either severe bucking or a no-start
Last quick thought is to ck that your Throttle Position Switch (TPS) is okay (continuity/no continuity) and adjusted to proper physical position